Tohoku Mathematical Journal Articles (Project Euclid)
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The latest articles from Tohoku Mathematical Journal on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2010 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Thu, 05 Aug 2010 15:41 EDTTue, 19 Apr 2011 09:33 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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$\boldsymbol{Q}$-factorial Gorenstein toric Fano varieties with large Picard number
http://projecteuclid.org/euclid.tmj/1270041023
<strong>Benjamin Nill</strong>, <strong>Mikkel Øbro</strong><p><strong>Source: </strong>Tohoku Math. J. (2), Volume 62, Number 1, 1--15.</p><p><strong>Abstract:</strong><br/>
In dimension $d$, ${\boldsymbol Q}$-factorial Gorenstein toric Fano varieties with
Picard number $\rho_X$ correspond to simplicial reflexive polytopes with $\rho_X +
d$ vertices. Casagrande showed that any $d$-dimensional simplicial reflexive
polytope has at most $3 d$ and $3d-1$ vertices if $d$ is even and odd, respectively.
Moreover, for $d$ even there is up to unimodular equivalence only one such polytope
with $3 d$ vertices, corresponding to the product of $d/2$ copies of a del Pezzo
surface of degree six. In this paper we completely classify all $d$-dimensional
simplicial reflexive polytopes having $3d-1$ vertices, corresponding to
$d$-dimensional ${\boldsymbol Q}$-factorial Gorenstein toric Fano varieties with
Picard number $2d-1$. For $d$ even, there exist three such varieties, with two being
singular, while for $d > 1$ odd there exist precisely two, both being nonsingular
toric fiber bundles over the projective line. This generalizes recent work of the
second author.
</p>projecteuclid.org/euclid.tmj/1270041023_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTGauss maps of toric varietieshttps://projecteuclid.org/euclid.tmj/1505181625<strong>Katsuhisa Furukawa</strong>, <strong>Atsushi Ito</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 69, Number 3, 431--454.</p><p><strong>Abstract:</strong><br/>
We investigate Gauss maps of (not necessarily normal) projective toric varieties
over an algebraically closed field of arbitrary characteristic. The main results
are as follows: (1) The structure of the Gauss map of a toric variety is
described in terms of combinatorics in any characteristic. (2) We give a
developability criterion in the toric case. In particular, we show that any
toric variety whose Gauss map is degenerate must be the join of some toric
varieties in characteristic zero. (3) As applications, we provide two
constructions of toric varieties whose Gauss maps have some given data (e.g.,
fibers, images) in positive characteristic.
</p>projecteuclid.org/euclid.tmj/1505181625_20170911220035Mon, 11 Sep 2017 22:00 EDTA remark on almost sure global well-posedness of the energy-critical defocusing
nonlinear wave equations in the periodic settinghttps://projecteuclid.org/euclid.tmj/1505181626<strong>Tadahiro Oh</strong>, <strong>Oana Pocovnicu</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 69, Number 3, 455--481.</p><p><strong>Abstract:</strong><br/>
In this note, we prove almost sure global well-posedness of the energy-critical
defocusing nonlinear wave equation on $\mathbb{T}^d$, $d = 3, 4,$ and $5$, with
random initial data below the energy space.
</p>projecteuclid.org/euclid.tmj/1505181626_20170911220035Mon, 11 Sep 2017 22:00 EDTBoundedness of the maximal operator on Musielak-Orlicz-Morrey spaceshttps://projecteuclid.org/euclid.tmj/1512183626<strong>Fumi-Yuki Maeda</strong>, <strong>Takao Ohno</strong>, <strong>Tetsu Shimomura</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 69, Number 4, 483--495.</p><p><strong>Abstract:</strong><br/>
We give the boundedness of the maximal operator on Musielak-Orlicz-Morrey spaces, which is an improvement of [7, Theorem 4.1]. We also discuss the sharpness of our conditions.
</p>projecteuclid.org/euclid.tmj/1512183626_20171201220054Fri, 01 Dec 2017 22:00 ESTBounds on the Tamagawa numbers of a crystalline representation over towers of cyclotomic extensionshttps://projecteuclid.org/euclid.tmj/1512183627<strong>Antonio Lei</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 69, Number 4, 497--524.</p><p><strong>Abstract:</strong><br/>
In this paper, we study the Tamagawa numbers of a crystalline representation over a tower of cyclotomic extensions under certain technical conditions on the representation. In particular, we show that we may improve the asymptotic bounds given in the thesis of Arthur Laurent in certain cases.
</p>projecteuclid.org/euclid.tmj/1512183627_20171201220054Fri, 01 Dec 2017 22:00 ESTHolomorphic isometric embeddings of the projective line into quadricshttps://projecteuclid.org/euclid.tmj/1512183628<strong>Oscar Macia</strong>, <strong>Yasuyuki Nagatomo</strong>, <strong>Masaro Takahashi</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 69, Number 4, 525--545.</p><p><strong>Abstract:</strong><br/>
We discuss holomorphic isometric embeddings of the projective line into quadrics using the generalisation of the theorem of do Carmo-Wallach in [14] to provide a description of their moduli spaces up to image and gauge equivalence. Moreover, we show rigidity of the real standard map from the projective line into quadrics.
</p>projecteuclid.org/euclid.tmj/1512183628_20171201220054Fri, 01 Dec 2017 22:00 ESTMonodromy representations of hypergeometric systems with respect to fundamental series solutionshttps://projecteuclid.org/euclid.tmj/1512183629<strong>Keiji Matsumoto</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 69, Number 4, 547--570.</p><p><strong>Abstract:</strong><br/>
We study the monodromy representation of the generalized hypergeometric differential equation and that of Lauricella's $F_C$ system of hypergeometric differential equations. We use fundamental systems of solutions expressed by the hypergeometric series. We express non-diagonal circuit matrices as reflections with respect to root vectors with all entries 1. We present a simple way to obtain circuit matrices.
</p>projecteuclid.org/euclid.tmj/1512183629_20171201220054Fri, 01 Dec 2017 22:00 ESTA polynomial defined by the $SL(2;\mathbb{C})$-Reidemeister torsion for a homology 3-sphere obtained by a Dehn surgery along a $(2p,q)$-torus knothttps://projecteuclid.org/euclid.tmj/1512183630<strong>Teruaki Kitano</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 69, Number 4, 571--583.</p><p><strong>Abstract:</strong><br/>
Let $K$ be a $(2p,q)$-torus knot. Here $p$ and $q$ are coprime odd positive integers. Let $M_n$ be a 3-manifold obtained by a $1/n$-Dehn surgery along $K$. We consider a polynomial $\sigma_{(2p,q,n)}(t)$ whose zeros are the inverses of the Reidemeister torsion of $M_n$ for $\mathit{SL}(2;\mathbb{C})$-irreducible representations under some normalization. Johnson gave a formula for the case of the $(2,3)$-torus knot under another normalization. We generalize this formula for the case of $(2p,q)$-torus knots by using Tchebychev polynomials.
</p>projecteuclid.org/euclid.tmj/1512183630_20171201220054Fri, 01 Dec 2017 22:00 ESTSpectral zeta functions of graphs and the Riemann zeta function in the critical striphttps://projecteuclid.org/euclid.tmj/1512183631<strong>Fabien Friedli</strong>, <strong>Anders Karlsson</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 69, Number 4, 585--610.</p><p><strong>Abstract:</strong><br/>
We initiate the study of spectral zeta functions $\zeta_X$ for finite and infinite graphs $X$, instead of the Ihara zeta function, with a perspective towards zeta functions from number theory and connections to hypergeometric functions. The Riemann hypothesis is shown to be equivalent to an approximate functional equation of graph zeta functions. The latter holds at all points where Riemann's zeta function $\zeta(s)$ is non-zero. This connection arises via a detailed study of the asymptotics of the spectral zeta functions of finite torus graphs in the critcal strip and estimates on the real part of the logarithmic derivative of $\zeta(s)$. We relate $\zeta_{\mathbb{Z}}$ to Euler's beta integral and show how to complete it giving the functional equation $\xi_{\mathbb{Z}}(1-s)=\xi_{\mathbb{Z}}(s)$. This function appears in the theory of Eisenstein series although presumably with this spectral intepretation unrecognized. In higher dimensions $d$ we provide a meromorphic continuation of $\zeta_{\mathbb{Z}^d}(s)$ to the whole plane and identify the poles. From our aymptotics several known special values of $\zeta(s)$ are derived as well as its non-vanishing on the line $Re(s)=1$. We determine the spectral zeta functions of regular trees and show it to be equal to a specialization of Appell's hypergeometric function $F_1$ via an Euler-type integral formula due to Picard.
</p>projecteuclid.org/euclid.tmj/1512183631_20171201220054Fri, 01 Dec 2017 22:00 ESTSchottky via the punctual Hilbert schemehttps://projecteuclid.org/euclid.tmj/1512183632<strong>Martin G. Gulbrandsen</strong>, <strong>Martí Lahoz</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 69, Number 4, 611--619.</p><p><strong>Abstract:</strong><br/>
We show that a smooth projective curve of genus $g$ can be reconstructed from its polarized Jacobian $(X, \Theta)$ as a certain locus in the Hilbert scheme $\mathrm{Hilb}^d(X)$, for $d=3$ and for $d=g+2$, defined by geometric conditions in terms of the polarization $\Theta$. The result is an application of the Gunning-Welters trisecant criterion and the Castelnuovo-Schottky theorem by Pareschi-Popa and Grushevsky, and its scheme theoretic extension by the authors.
</p>projecteuclid.org/euclid.tmj/1512183632_20171201220054Fri, 01 Dec 2017 22:00 ESTMinimal timelike surfaces in a certain homogeneous Lorentzian 3-manifoldhttps://projecteuclid.org/euclid.tmj/1512183633<strong>Sungwook Lee</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 69, Number 4, 621--635.</p><p><strong>Abstract:</strong><br/>
The 2-parameter family of certain homogeneous Lorentzian 3-manifolds which includes Minkowski 3-space, de Sitter 3-space, and Minkowski motion group is considered. Each homogeneous Lorentzian 3-manifold in the 2-parameter family has a solvable Lie group structure with left invariant metric. A generalized integral representation formula which is the unification of representation formulas for minimal timelike surfaces in those homogeneous Lorentzian 3-manifolds is obtained. The normal Gauß map of minimal timelike surfaces in those homogeneous Lorentzian 3-manifolds and its harmonicity are discussed.
</p>projecteuclid.org/euclid.tmj/1512183633_20171201220054Fri, 01 Dec 2017 22:00 ESTOn the most expected number of components for random linkshttps://projecteuclid.org/euclid.tmj/1512183634<strong>Kazuhiro Ichihara</strong>, <strong>Ken-ichi Yoshida</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 69, Number 4, 637--641.</p><p><strong>Abstract:</strong><br/>
We consider a random link, which is defined as the closure of a braid obtained from a random walk on the braid group. For such a random link, the expected value for the number of components was calculated by Jiming Ma. In this paper, we determine the most expected number of components for a random link, and further, consider the most expected partition of the number of strings for a random braid.
</p>projecteuclid.org/euclid.tmj/1512183634_20171201220054Fri, 01 Dec 2017 22:00 ESTExponentially weighted Polynomial approximation for absolutely continuous functionshttps://projecteuclid.org/euclid.tmj/1520564416<strong>Kentaro Itoh</strong>, <strong>Ryozi Sakai</strong>, <strong>Noriaki Suzuki</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 1, 1--15.</p><p><strong>Abstract:</strong><br/>
We discuss a polynomial approximation on $\mathbb{R}$ with a weight $w$ in $\mathcal{F}(C^{2} +)$ (see Section 2). The de la Vallée Poussin mean $v_n(f)$ of an absolutely continuous function $f$ is not only a good approximation polynomial of $f$, but also its derivatives give an approximation for the derivative $f'$. More precisely, for $1 \leq p \leq \infty$, we have $\lim_{n \rightarrow \infty}\|(f - v_{n}(f))w\|_{L^{p}(\mathbb{R})} =0$ and $\lim_{n \rightarrow \infty}\|(f' - v_{n}(f)')w\|_{L^{p}(\mathbb{R})} =0$ whenever $f''w \in L^{p}(\mathbb{R})$.
</p>projecteuclid.org/euclid.tmj/1520564416_20180308220031Thu, 08 Mar 2018 22:00 ESTOn Frobenius manifolds from Gromov–Witten theory of orbifold projective lines with $r$ orbifold pointshttps://projecteuclid.org/euclid.tmj/1520564417<strong>Yuuki Shiraishi</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 1, 17--37.</p><p><strong>Abstract:</strong><br/>
We prove that the Frobenius structure constructed from the Gromov–Witten theory for an orbifold projective line with at most $r$ orbifold points is uniquely determined by the WDVV equations with certain natural initial conditions.
</p>projecteuclid.org/euclid.tmj/1520564417_20180308220031Thu, 08 Mar 2018 22:00 ESTWorpitzky partitions for root systems and characteristic quasi-polynomialshttps://projecteuclid.org/euclid.tmj/1520564418<strong>Masahiko Yoshinaga</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 1, 39--63.</p><p><strong>Abstract:</strong><br/>
For a given irreducible root system, we introduce a partition of (coweight) lattice points inside the dilated fundamental parallelepiped into those of partially closed simplices. This partition can be considered as a generalization and a lattice points interpretation of the classical formula of Worpitzky.
This partition, and the generalized Eulerian polynomial, recently introduced by Lam and Postnikov, can be used to describe the characteristic (quasi)polynomials of Shi and Linial arrangements. As an application, we prove that the characteristic quasi-polynomial of the Shi arrangement turns out to be a polynomial. We also present several results on the location of zeros of characteristic polynomials, related to a conjecture of Postnikov and Stanley. In particular, we verify the “functional equation” of the characteristic polynomial of the Linial arrangement for any root system, and give partial affirmative results on “Riemann hypothesis” for the root systems of type $E_6, E_7, E_8$, and $F_4$.
</p>projecteuclid.org/euclid.tmj/1520564418_20180308220031Thu, 08 Mar 2018 22:00 ESTThe rates of the $L^p$-convergence of the Euler-Maruyama and Wong-Zakai approximations of path-dependent stochastic differential equations under the Lipschitz conditionhttps://projecteuclid.org/euclid.tmj/1520564419<strong>Shigeki Aida</strong>, <strong>Takanori Kikuchi</strong>, <strong>Seiichiro Kusuoka</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 1, 65--95.</p><p><strong>Abstract:</strong><br/>
We consider the rates of the $L^p$-convergence of the Euler-Maruyama and Wong-Zakai approximations of path-dependent stochastic differential equations under the Lipschitz condition on the coefficients. By a transformation, the stochastic differential equations of Markovian type with reflecting boundary condition on sufficiently good domains are to be associated with the equations concerned in the present paper. The obtained rates of the $L^p$-convergence are the same as those in the case of the stochastic differential equations of Markovian type without boundaries.
</p>projecteuclid.org/euclid.tmj/1520564419_20180308220031Thu, 08 Mar 2018 22:00 ESTStochastic calculus for Markov processes associated with semi-Dirichlet formshttps://projecteuclid.org/euclid.tmj/1520564420<strong>Chuan-Zhong Chen</strong>, <strong>Li Ma</strong>, <strong>Wei Sun</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 1, 97--119.</p><p><strong>Abstract:</strong><br/>
We present a new Fukushima type decomposition in the framework of semi-Dirichlet forms. This generalizes the result of Ma, Sun and Wang [17, Theorem 1.4] by removing the condition (S). We also extend Nakao's integral to semi-Dirichlet forms and derive Itô's formula related to it.
</p>projecteuclid.org/euclid.tmj/1520564420_20180308220031Thu, 08 Mar 2018 22:00 ESTSharp $L^p$-bounds for the martingale maximal functionhttps://projecteuclid.org/euclid.tmj/1520564421<strong>Adam Osȩkowski</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 1, 121--138.</p><p><strong>Abstract:</strong><br/>
The paper studies sharp weighted $L^p$ inequalities for the martingale maximal function. Proofs exploit properties of certain special functions of four variables and self-improving properties of $A_p$ weights.
</p>projecteuclid.org/euclid.tmj/1520564421_20180308220031Thu, 08 Mar 2018 22:00 ESTA coupling of Brownian motions in the $\mathcal{L}_0$-geometryhttps://projecteuclid.org/euclid.tmj/1520564422<strong>Takafumi Amaba</strong>, <strong>Kazumasa Kuwada</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 1, 139--174.</p><p><strong>Abstract:</strong><br/>
Under a complete Ricci flow, we construct a coupling of two Brownian motions such that their $\mathcal{L}_0$-distance is a supermartingale. This recovers a result of Lott [J. Lott, Optimal transport and Perelman's reduced volume, Calc. Var. Partial Differential Equations 36 (2009), no. 1, 49–84.] on the monotonicity of $\mathcal{L}_0$-distance between heat distributions.
</p>projecteuclid.org/euclid.tmj/1520564422_20180308220031Thu, 08 Mar 2018 22:00 ESTA control theorem for the torsion Selmer pointed sethttps://projecteuclid.org/euclid.tmj/1527904820<strong>Kenji Sakugawa</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 2, 175--223.</p><p><strong>Abstract:</strong><br/>
Minhyong Kim defined the Selmer variety associated with a curve $X$ over a number field, which is a non-abelian analogue of the ${\mathbb Q}_p$-Selmer group of the Jacobian variety of $X$. In this paper, we define a torsion analogue of the Selmer variety. Recall that Mazur's control theorem describes the behavior of the torsion Selmer groups of an abelian variety with good ordinary reduction at $p$ in the cyclotomic tower of number fields. We give a non-abelian analogue of Mazur's control theorem by replacing the torsion Selmer group by a torsion analogue of the Selmer variety.
</p>projecteuclid.org/euclid.tmj/1527904820_20180601220029Fri, 01 Jun 2018 22:00 EDTThe primitive spectrum for $\mathfrak{gl}(m|n)$https://projecteuclid.org/euclid.tmj/1527904821<strong>Kevin Coulembier</strong>, <strong>Ian M. Musson</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 2, 225--266.</p><p><strong>Abstract:</strong><br/>
We study inclusions between primitive ideals in the universal enveloping algebra of general linear superalgebras. For classical simple Lie superalgebras, any primitive ideal is the annihilator of a simple highest weight module. It therefore suffices to study the quasi-order on highest weights determined by the relation of inclusion between primitive ideals. For the specific case of reductive Lie algebras, this quasi-order is essentially the left Kazhdan-Lusztig quasi-order. For Lie superalgebras, a description of the poset structure on the set primitive ideals is at the moment not known, apart from some low dimensional specific cases. We derive an alternative definition of the left Kazhdan-Lusztig quasi-order which extends to classical Lie superalgebras. We denote this quasi-order by $\unlhd$ and show that a relation in $\unlhd$ implies an inclusion between primitive ideals.
For $\mathfrak{gl}(m|n)$ the new quasi-order $\unlhd$ is defined explicitly in terms of Brundan's Kazhdan-Lusztig theory. We prove that $\unlhd$ induces an actual partial order on the set of primitive ideals. We conjecture that this is the inclusion order. By the above paragraph one direction of this conjecture is true. We prove several consistency results concerning the conjecture and prove it for singly atypical and typical blocks of $\mathfrak{gl}(m|n)$ and in general for $\mathfrak{gl}(2|2)$. An important tool is a new translation principle for primitive ideals, based on the crystal structure underlying Brundan's categorification on category ${\mathcal O}$. Finally we focus on an interesting explicit example; the poset of primitive ideals contained in the augmentation ideal for $\mathfrak{gl}(m|1)$.
</p>projecteuclid.org/euclid.tmj/1527904821_20180601220029Fri, 01 Jun 2018 22:00 EDTClosed three-dimensional Alexandrov spaces with isometric circle actionshttps://projecteuclid.org/euclid.tmj/1527904822<strong>Jesús Núñez-Zimbrón</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 2, 267--284.</p><p><strong>Abstract:</strong><br/>
We obtain a topological and weakly equivariant classification of closed three-dimensional Alexandrov spaces with an effective, isometric circle action. This generalizes the topological and equivariant classifications of Raymond [26] and Orlik and Raymond [23] of closed three-dimensional manifolds admitting an effective circle action. As an application, we prove a version of the Borel conjecture for closed three-dimensional Alexandrov spaces with circle symmetry.
</p>projecteuclid.org/euclid.tmj/1527904822_20180601220029Fri, 01 Jun 2018 22:00 EDTThree consecutive approximation coefficients: asymptotic frequencies in semi-regular caseshttps://projecteuclid.org/euclid.tmj/1527904823<strong>Jaap de Jonge</strong>, <strong>Cor Kraaikamp</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 2, 285--317.</p><p><strong>Abstract:</strong><br/>
Denote by $p_n/q_n, n=1,2,3,\ldots,$ the sequence of continued fraction convergents of a real irrational number $x$. Define the sequence of approximation coefficients by $\theta_n(x):=q_n\left|q_nx-p_n\right|, n=1,2,3,\ldots$. In the case of regular continued fractions the six possible patterns of three consecutive approximation coefficients, such as $\theta_{n-1}<\theta_n<\theta_{n+1}$, occur for almost all $x$ with only two different asymptotic frequencies. In this paper it is shown how these asymptotic frequencies can be determined for two other semi-regular cases. It appears that the optimal continued fraction has a similar distribution of only two asymptotic frequencies, albeit with different values. The six different values that are found in the case of the nearest integer continued fraction will show to be closely related to those of the optimal continued fraction.
</p>projecteuclid.org/euclid.tmj/1527904823_20180601220029Fri, 01 Jun 2018 22:00 EDTModules of bilinear differential operators over the orthosymplectic superalgebra $\mathfrak{osp}(1|2)$https://projecteuclid.org/euclid.tmj/1527904824<strong>Taher Bichr</strong>, <strong>Jamel Boujelben</strong>, <strong>Khaled Tounsi</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 2, 319--338.</p><p><strong>Abstract:</strong><br/>
Let $\frak{F}_\lambda, \lambda\in \mathbb{C}$, be the space of tensor densities of degree $\lambda$ on the supercircle $S^{1|1}$. We consider the superspace $\mathfrak{D}_{\lambda_1,\lambda_2,\mu}$ of bilinear differential operators from $\frak{F}_{\lambda_1}\otimes\frak{F}_{\lambda_2}$ to $\frak{F}_{\mu}$ as a module over the orthosymplectic superalgebra $\mathfrak{osp}(1|2)$. We prove the existence and the uniqueness of a canonical conformally equivariant symbol map from $\mathfrak{D}_{\lambda_1,\lambda_2,\mu}^k$ to the corresponding space of symbols. An explicit expression of the associated quantization map is also given.
</p>projecteuclid.org/euclid.tmj/1527904824_20180601220029Fri, 01 Jun 2018 22:00 EDTOn a class of singular superlinear elliptic systems in a ballhttps://projecteuclid.org/euclid.tmj/1537495350<strong>Dang Dinh Hai</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 3, 339--352.</p><p><strong>Abstract:</strong><br/>
We establish the existence of large positive radial solutions for the elliptic system $$ \left\{ \begin{array}{c} -\Delta u=\lambda f(v) \ \text{in} \ B\\ -\Delta v=\lambda g(u) \ \text{in} \ B\\ u=v=0 \ \text{on} \ \partial B \end{array} \right. $$ when the parameter $\lambda>0$ is small, where $B$ is the open unit ball $\mathbb{R}^N,N>2, f,g:(0,\infty) \rightarrow \mathbb{R}$ are possibly singular at 0 and $f(u) \sim u^p,g(v) \sim v^q$ at $\infty$ for some $p,q>0$ with $pq>1$. Our approach is based on fixed point theory in a cone.
</p>projecteuclid.org/euclid.tmj/1537495350_20180920220248Thu, 20 Sep 2018 22:02 EDTPolar foliations on quaternionic projective spaceshttps://projecteuclid.org/euclid.tmj/1537495351<strong>Miguel Domínguez-Vázquez</strong>, <strong>Claudio Gorodski</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 3, 353--375.</p><p><strong>Abstract:</strong><br/>
We classify irreducible polar foliations of codimension $q$ on quaternionic projective spaces $\mathbb{H} P^n$, for all $(n,q)\neq(7,1)$. We prove that all irreducible polar foliations of any codimension (resp. of codimension one) on $\mathbb{H} P^n$ are homogeneous if and only if $n+1$ is a prime number (resp. $n$ is even or $n=1$). This shows the existence of inhomogeneous examples of codimension one and higher.
</p>projecteuclid.org/euclid.tmj/1537495351_20180920220248Thu, 20 Sep 2018 22:02 EDTAn elementary proof of Cohen-Gabber theorem in the equal characteristic $p>0$ casehttps://projecteuclid.org/euclid.tmj/1537495352<strong>Kazuhiko Kurano</strong>, <strong>Kazuma Shimomoto</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 3, 377--389.</p><p><strong>Abstract:</strong><br/>
The aim of this article is to give a new proof of Cohen-Gabber theorem in the equal characteristic $p>0$ case.
</p>projecteuclid.org/euclid.tmj/1537495352_20180920220248Thu, 20 Sep 2018 22:02 EDTThe isometry groups of compact manifolds with almost negative Ricci curvaturehttps://projecteuclid.org/euclid.tmj/1537495353<strong>Atsushi Katsuda</strong>, <strong>Takeshi Kobayashi</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 3, 391--400.</p><p><strong>Abstract:</strong><br/>
We estimate the order of isometry groups of compact Riemannian manifolds which have negative Ricci curvature except for small portions, in terms of geometric quantities.
</p>projecteuclid.org/euclid.tmj/1537495353_20180920220248Thu, 20 Sep 2018 22:02 EDTOn the rational cohomology of regular surfaces isogenous to a product of curves with $\chi(\mathcal{O}_S)=2$https://projecteuclid.org/euclid.tmj/1537495354<strong>Matteo A. Bonfanti</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 3, 401--423.</p><p><strong>Abstract:</strong><br/>
Let $S$ be a surface isogenous to a product of curves of unmixed type. After presenting several results useful to study the cohomology of $S$ we prove a structure theorem for the cohomology of regular surfaces isogenous to a product of unmixed type with $\chi (\mathcal{O}_S)=2$. In particular we found two families of surfaces of general type with maximal Picard number.
</p>projecteuclid.org/euclid.tmj/1537495354_20180920220248Thu, 20 Sep 2018 22:02 EDTThe equivalence of weak and very weak supersolutions to the porous medium equationhttps://projecteuclid.org/euclid.tmj/1537495355<strong>Pekka Lehtelä</strong>, <strong>Teemu Lukkari</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 3, 425--445.</p><p><strong>Abstract:</strong><br/>
We prove that various notions of supersolutions to the porous medium equation are equivalent under suitable conditions. More spesifically, we consider weak supersolutions, very weak supersolutions, and $m$-superporous functions defined via a comparison principle. The proofs are based on comparison principles and a Schwarz type alternating method, which are also interesting in their own right. Along the way, we show that Perron solutions with merely continuous boundary values are continuous up to the parabolic boundary of a sufficiently smooth space-time cylinder.
</p>projecteuclid.org/euclid.tmj/1537495355_20180920220248Thu, 20 Sep 2018 22:02 EDTDouble lines on quadric hypersurfaceshttps://projecteuclid.org/euclid.tmj/1537495356<strong>Edoardo Ballico</strong>, <strong>Sukmoon Huh</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 3, 447--473.</p><p><strong>Abstract:</strong><br/>
We study double line structures in projective spaces and quadric hypersurfaces, and investigate the geometry of irreducible components of Hilbert scheme of curves and moduli of stable sheaves of pure dimension 1 on a smooth quadric threefold.
</p>projecteuclid.org/euclid.tmj/1537495356_20180920220248Thu, 20 Sep 2018 22:02 EDTParallel mean curvature tori in $\mathbb{C}P^{2}$ and $\mathbb{C}H^{2}$https://projecteuclid.org/euclid.tmj/1537495357<strong>Katsuei Kenmotsu</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 3, 475--485.</p><p><strong>Abstract:</strong><br/>
We explicitly determine tori that have a parallel mean curvature vector, both in the complex projective plane and the complex hyperbolic plane.
</p>projecteuclid.org/euclid.tmj/1537495357_20180920220248Thu, 20 Sep 2018 22:02 EDTPseudo-Hermitian manifolds with automorphism group of maximal dimensionhttps://projecteuclid.org/euclid.tmj/1546570822<strong>Jae-Cheon Joo</strong>, <strong>Kang-Hyurk Lee</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 4, 487--510.</p><p><strong>Abstract:</strong><br/>
This paper concerns a local characterization of 5-dimensional pseudo-Hermitian manifolds with maximal automorphism group in the case the underlying almost CR structures are not integrable. We also present examples of globally homogeneous model of maximal dimensional automorphism group.
</p>projecteuclid.org/euclid.tmj/1546570822_20190103220047Thu, 03 Jan 2019 22:00 ESTOn the K-stability of Fano varieties and anticanonical divisorshttps://projecteuclid.org/euclid.tmj/1546570823<strong>Kento Fujita</strong>, <strong>Yuji Odaka</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 4, 511--521.</p><p><strong>Abstract:</strong><br/>
We apply a recent theorem of Li and the first author to give some criteria for the K-stability of Fano varieties in terms of anticanonical $\mathbb{Q}$-divisors. First, we propose a condition in terms of certain anti-canonical $\mathbb{Q}$-divisors of given Fano variety, which we conjecture to be equivalent to the K-stability. We prove that it is at least a sufficient condition and also related to the Berman-Gibbs stability. We also give another algebraic proof of the K-stability of Fano varieties which satisfy Tian's alpha invariants condition.
</p>projecteuclid.org/euclid.tmj/1546570823_20190103220047Thu, 03 Jan 2019 22:00 ESTThe structure of the space of polynomial solutions to the canonical central systems of differential equations on the block Heisenberg groups: A generalization of a theorem of Korányihttps://projecteuclid.org/euclid.tmj/1546570824<strong>Anthony C. Kable</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 4, 523--545.</p><p><strong>Abstract:</strong><br/>
A result of Korányi that describes the structure of the space of polynomial solutions to the Heisenberg Laplacian operator is generalized to the canonical central systems on the block Heisenberg groups. These systems of differential operators generalize the Heisenberg Laplacian and, like it, admit large algebras of conformal symmetries. The main result implies that in most cases all polynomial solutions can be obtained from a single one by the repeated application of conformal symmetry operators.
</p>projecteuclid.org/euclid.tmj/1546570824_20190103220047Thu, 03 Jan 2019 22:00 EST$\sigma$-actions and symmetric triadshttps://projecteuclid.org/euclid.tmj/1546570825<strong>Osamu Ikawa</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 4, 547--565.</p><p><strong>Abstract:</strong><br/>
For a given compact connected Lie group and an involution on it, we can define a hyperpolar action. We study the orbit space and the properties of each orbit of the action. The result is a natural extension of maximal torus theory.
</p>projecteuclid.org/euclid.tmj/1546570825_20190103220047Thu, 03 Jan 2019 22:00 ESTWavelets in weighted norm spaceshttps://projecteuclid.org/euclid.tmj/1546570826<strong>Kazaros S. Kazarian</strong>, <strong>Samvel S. Kazaryan</strong>, <strong>Angel San Antolín</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 4, 567--605.</p><p><strong>Abstract:</strong><br/>
We give a complete characterization of the classes of weight functions for which the higher rank Haar wavelet systems are unconditional bases in weighted norm Lebesgue spaces. Particulary it follows that higher rank Haar wavelets are unconditional bases in the weighted norm spaces with weights which have strong zeros at some points. This shows that the class of weight functions for which higher rank Haar wavelets are unconditional bases is much richer than it was supposed.
</p>projecteuclid.org/euclid.tmj/1546570826_20190103220047Thu, 03 Jan 2019 22:00 ESTTeichmüller spaces and tame quasiconformal motionshttps://projecteuclid.org/euclid.tmj/1546570827<strong>Yunping Jiang</strong>, <strong>Sudeb Mitra</strong>, <strong>Hiroshige Shiga</strong>, <strong>Zhe Wang</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 4, 607--631.</p><p><strong>Abstract:</strong><br/>
The concept of “quasiconformal motion” was first introduced by Sullivan and Thurston (in [24]). Theorem 3 of that paper asserted that any quasiconformal motion of a set in the sphere over an interval can be extended to the sphere. In this paper, we give a counter-example to that assertion. We introduce a new concept called “tame quasiconformal motion” and show that their assertion is true for tame quasiconformal motions. We prove a much more general result that, any tame quasiconformal motion of a closed set in the sphere, over a simply connected Hausdorff space, can be extended as a quasiconformal motion of the sphere. Furthermore, we show that this extension can be done in a conformally natural way. The fundamental idea is to show that the Teichmüller space of a closed set in the sphere is a “universal parameter space” for tame quasiconformal motions of that set over a simply connected Hausdorff space.
</p>projecteuclid.org/euclid.tmj/1546570827_20190103220047Thu, 03 Jan 2019 22:00 ESTLarge deviations for continuous additive functionals of symmetric Markov processeshttps://projecteuclid.org/euclid.tmj/1546570828<strong>Seunghwan Yang</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 70, Number 4, 633--648.</p><p><strong>Abstract:</strong><br/>
Let $X$ be a locally compact separable metric space and $m$ a positive Radon measure on $X$ with full topological support. Let ${\bf{M}}=(P_x,X_t)$ be an $m$-symmetric Markov process on $X$. Let $(\mathcal{E},\mathcal{D}(\mathcal{E}))$ be the Dirichlet form on $L^2(X;m)$ generated by ${\bf{M}}$. Let $\mu$ be a positive Radon measure in the Green-tight Kato class and $A^\mu_t$ the positive continuous additive functional in the Revuz correspondence to $\mu$. Under certain conditions, we establish the large deviation principle for positive continuous additive functionals $A^\mu_t$ of symmetric Markov processes.
</p>projecteuclid.org/euclid.tmj/1546570828_20190103220047Thu, 03 Jan 2019 22:00 ESTOrthogonality of divisorial Zariski decompositions for classes with volume zerohttps://projecteuclid.org/euclid.tmj/1552100439<strong>Valentino Tosatti</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 1, 1--8.</p><p><strong>Abstract:</strong><br/>
We show that the orthogonality conjecture for divisorial Zariski decompositions on compact Kähler manifolds holds for pseudoeffective (1,1) classes with volume zero.
</p>projecteuclid.org/euclid.tmj/1552100439_20190308220117Fri, 08 Mar 2019 22:01 ESTInfinite particle systems of long range jumps with long range interactionshttps://projecteuclid.org/euclid.tmj/1552100440<strong>Syota Esaki</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 1, 9--33.</p><p><strong>Abstract:</strong><br/>
In this paper a general theorem for constructing infinite particle systems of jump type with long range interactions is presented. It can be applied to the system that each particle undergoes an $\alpha$-stable process and interaction between particles is given by the logarithmic potential appearing random matrix theory or potentials of Ruelle's class with polynomial decay. It is shown that the system can be constructed for any $\alpha \in (0, 2)$ if its equilibrium measure $\mu$ is translation invariant, and $\alpha$ is restricted by the growth order of the 1-correlation function of the measure $\mu$ in general case.
</p>projecteuclid.org/euclid.tmj/1552100440_20190308220117Fri, 08 Mar 2019 22:01 ESTRational orbits of primitive trivectors in dimension sixhttps://projecteuclid.org/euclid.tmj/1552100441<strong>Akihiko Yukie</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 1, 35--52.</p><p><strong>Abstract:</strong><br/>
Let $G=\operatorname{GL}(1)\times \mathrm{GSp}(6)$ and $V$ be the irreducible representation of $G$ of dimension 14 over a field of characteristic not equal to 2,3. This is an irreducible prehomogeneous vector space. We determine generic rational orbits and their stabilizers of this prehomogeneous vector space.
</p>projecteuclid.org/euclid.tmj/1552100441_20190308220117Fri, 08 Mar 2019 22:01 ESTObstacle problem for Musielak-Orlicz Dirichlet energy integral on metric measure spaceshttps://projecteuclid.org/euclid.tmj/1552100442<strong>Fumi-Yuki Maeda</strong>, <strong>Takao Ohno</strong>, <strong>Tetsu Shimomura</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 1, 53--68.</p><p><strong>Abstract:</strong><br/>
We introduce Musielak-Orlicz Newtonian space on a metric measure space. After discussing properties of weak upper gradients of functions in such spaces and Poincaré inequalities for functions with zero boundary values in bounded open subsets, we prove the existence and uniqueness of a solution to an obstacle problem for Musielak-Orlicz Dirichlet energy integral.
</p>projecteuclid.org/euclid.tmj/1552100442_20190308220117Fri, 08 Mar 2019 22:01 ESTRigidity of manifolds with boundary under a lower Bakry-Émery Ricci curvature boundhttps://projecteuclid.org/euclid.tmj/1552100443<strong>Yohei Sakurai</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 1, 69--109.</p><p><strong>Abstract:</strong><br/>
We study Riemannian manifolds with boundary under a lower Bakry-Émery Ricci curvature bound. In our weighted setting, we prove several rigidity theorems for such manifolds with boundary. We conclude a rigidity theorem for the inscribed radii, a volume growth rigidity theorem for the metric neighborhoods of the boundaries, and various splitting theorems. We also obtain rigidity theorems for the smallest Dirichlet eigenvalues for the weighted $p$-Laplacians.
</p>projecteuclid.org/euclid.tmj/1552100443_20190308220117Fri, 08 Mar 2019 22:01 ESTThe $\boldsymbol{p}$-adic duality for the finite star-multiple polylogarithmshttps://projecteuclid.org/euclid.tmj/1552100444<strong>Shin-ichiro Seki</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 1, 111--122.</p><p><strong>Abstract:</strong><br/>
We prove the $\boldsymbol{p}$-adic duality theorem for the finite star-multiple polylogarithms. That is a generalization of Hoffman's duality theorem for the finite multiple zeta-star values.
</p>projecteuclid.org/euclid.tmj/1552100444_20190308220117Fri, 08 Mar 2019 22:01 ESTCharacterization of 2-dimensional normal Mather-Jacobian log canonical singularitieshttps://projecteuclid.org/euclid.tmj/1552100445<strong>Kohsuke Shibata</strong>, <strong>Nguyen Duc Tam</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 1, 123--136.</p><p><strong>Abstract:</strong><br/>
In this paper we characterize 2-dimensional normal Mather-Jacobian log canonical singularities which are not complete intersections. We prove that a 2-dimensional normal singularity which is not a complete intersection is a Mather-Jacobian log canonical singularity if and only if it is a toric singularity with embedding dimension 4.
</p>projecteuclid.org/euclid.tmj/1552100445_20190308220117Fri, 08 Mar 2019 22:01 ESTToric Fano varieties associated to finite simple graphshttps://projecteuclid.org/euclid.tmj/1552100446<strong>Yusuke Suyama</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 1, 137--144.</p><p><strong>Abstract:</strong><br/>
We give a necessary and sufficient condition for the nonsingular projective toric variety associated to a finite simple graph to be Fano or weak Fano in terms of the graph.
</p>projecteuclid.org/euclid.tmj/1552100446_20190308220117Fri, 08 Mar 2019 22:01 ESTA generalized maximal diameter sphere theoremhttps://projecteuclid.org/euclid.tmj/1552100447<strong>Nathaphon Boonnam</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 1, 145--155.</p><p><strong>Abstract:</strong><br/>
We prove that if a complete connected $n$-dimensional Riemannian manifold $M$ has radial sectional curvature at a base point $p\in M$ bounded from below by the radial curvature function of a two-sphere of revolution $\widetilde M$ belonging to a certain class, then the diameter of $M$ does not exceed that of $\widetilde M$. Moreover, we prove that if the diameter of $M$ equals that of $\widetilde M$, then $M$ is isometric to the $n$-model of $\widetilde M$. The class of a two-sphere of revolution employed in our main theorem is very wide. For example, this class contains both ellipsoids of prolate type and spheres of constant sectional curvature. Thus our theorem contains both the maximal diameter sphere theorem proved by Toponogov [9] and the radial curvature version by the present author [2] as a corollary.
</p>projecteuclid.org/euclid.tmj/1552100447_20190308220117Fri, 08 Mar 2019 22:01 ESTClassification of biharmonic $\mathcal{C}$-parallel Legendrian submanifolds in 7-dimensional Sasakian space formshttps://projecteuclid.org/euclid.tmj/1552100448<strong>Toru Sasahara</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 1, 157--169.</p><p><strong>Abstract:</strong><br/>
In [5], D. Fetcu and C. Oniciuc presented the classification result for biharmonic $\mathcal{C}$-parallel Legendrian submanifolds in 7-dimensional Sasakian space forms. However, it is incomplete. In this paper, all such submanifolds are explicitly determined.
</p>projecteuclid.org/euclid.tmj/1552100448_20190308220117Fri, 08 Mar 2019 22:01 ESTCharacteristic cycles of highest weight Harish-Chandra modules and the Weyl group action on the conormal varietyhttps://projecteuclid.org/euclid.tmj/1561082595<strong>Leticia Barchini</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 2, 171--205.</p><p><strong>Abstract:</strong><br/>
We give an inductive algorithm that computes the action of simple reflections on a subset of basis-vectors of the Borel-Moore homology of the conormal variety associated to the symmetric pair $(\text{Sp}(2n), \text{GL}(n))$.
</p>projecteuclid.org/euclid.tmj/1561082595_20190620220336Thu, 20 Jun 2019 22:03 EDTQuinary lattices and binary quaternion hermitian latticeshttps://projecteuclid.org/euclid.tmj/1561082596<strong>Tomoyoshi Ibukiyama</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 2, 207--220.</p><p><strong>Abstract:</strong><br/>
In our previous papers, we defined the $G$-type number of any genera of quaternion hermitian lattices as a generalization of the type number of a quaternion algebra. Now we prove in this paper that the $G$-type number of any genus of positive definite binary quaternion hermitian maximal lattices in $B^2$ for a definite quaternion algebra $B$ over $\mathbb Q$ is equal to the class number of some explicitly defined genus of positive definite quinary quadratic lattices. This is a generalization of a part of the results in 1982, where only the principal genus was treated. Explicit formulas for this type number can be obtained by using Asai's class number formula. In particular, in case when the discriminant of $B$ is a prime, we will write down an explicit formula for $T$, $H$ and $2T-H$ for the non-principal genus, where $T$ and $H$ are the type number and the class number. This number was known for the principal genus before. In another paper, our new result is applied to polarized superspecial varieties and irreducible components of supersingular locus in the moduli of principally polarized abelian varieties having a model over a finite prime field, where $2T-H$ plays an important role.
</p>projecteuclid.org/euclid.tmj/1561082596_20190620220336Thu, 20 Jun 2019 22:03 EDTThe conservativeness of Girsanov transformed symmetric Markov processeshttps://projecteuclid.org/euclid.tmj/1561082597<strong>Yusuke Miura</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 2, 221--241.</p><p><strong>Abstract:</strong><br/>
In this paper, we study those Girsanov transformations of symmetric Markov processes which preserve the symmetry. Employing a criterion for uniform integrability of exponential martingales due to Chen [3], we identify the class of transformations which transform the original process into a conservative one, even if the original one is explosive. We also consider the class of transformations which transform to a recurrent one. In [14, 22], the same problems are studied for symmetric diffusion processes. Our main theorem is an extension of their results to symmetric Markov processes with jumps.
</p>projecteuclid.org/euclid.tmj/1561082597_20190620220336Thu, 20 Jun 2019 22:03 EDTSteady states of FitzHugh-Nagumo system with non-diffusive activator and diffusive inhibitorhttps://projecteuclid.org/euclid.tmj/1561082598<strong>Ying Li</strong>, <strong>Anna Marciniak-Czochra</strong>, <strong>Izumi Takagi</strong>, <strong>Boying Wu</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 2, 243--279.</p><p><strong>Abstract:</strong><br/>
In this paper, we consider a diffusion equation coupled to an ordinary differential equation with FitzHugh-Nagumo type nonlinearity. We construct continuous spatially heterogeneous steady states near, as well as far from, constant steady states and show that they are all unstable. In addition, we construct various types of steady states with jump discontinuities and prove that they are stable in a weak sense defined by Weinberger.The results are quite different from those for classical reaction-diffusion systems where all species diffuse.
</p>projecteuclid.org/euclid.tmj/1561082598_20190620220336Thu, 20 Jun 2019 22:03 EDTProducts of random walks on finite groups with moderate growthhttps://projecteuclid.org/euclid.tmj/1561082599<strong>Guan-Yu Chen</strong>, <strong>Takashi Kumagai</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 2, 281--302.</p><p><strong>Abstract:</strong><br/>
In this article, we consider products of random walks on finite groups with moderate growth and discuss their cutoffs in the total variation. Based on several comparison techniques, we are able to identify the total variation cutoff of discrete time lazy random walks with the Hellinger distance cutoff of continuous time random walks. Along with the cutoff criterion for Laplace transforms, we derive a series of equivalent conditions on the existence of cutoffs, including the existence of pre-cutoffs, Peres' product condition and a formula generated by the graph diameters. For illustration, we consider products of Heisenberg groups and randomized products of finite cycles.
</p>projecteuclid.org/euclid.tmj/1561082599_20190620220336Thu, 20 Jun 2019 22:03 EDTA revisit on commutators of linear and bilinear fractional integral operatorhttps://projecteuclid.org/euclid.tmj/1561082600<strong>Mingming Cao</strong>, <strong>Qingying Xue</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 2, 303--318.</p><p><strong>Abstract:</strong><br/>
Let $I_{\alpha}$ be the linear and $\mathcal{I}_{\alpha}$ be the bilinear fractional integral operators. In the linear setting, it is known that the two-weight inequality holds for the first order commutators of $I_{\alpha}$. But the method can't be used to obtain the two weighted norm inequality for the higher order commutators of $I_{\alpha}$. In this paper, using some known results, we first give an alternative simple proof for the first order commutators of $I_{\alpha}$. This new approach allows us to consider the higher order commutators. Then, by using the Cauchy integral theorem, we show that the two-weight inequality holds for the higher order commutators of $I_{\alpha}$. In the bilinear setting, we present a dyadic proof for the characterization between $BMO$ and the boundedness of $[b,\mathcal{I}_{\alpha}]$. Moreover, some bilinear paraproducts are also treated in order to obtain the boundedness of $[b,\mathcal{I}_{\alpha}]$.
</p>projecteuclid.org/euclid.tmj/1561082600_20190620220336Thu, 20 Jun 2019 22:03 EDTA flat projective variety with $D_8$-holonomyhttps://projecteuclid.org/euclid.tmj/1561082601<strong>Francis E. A. Johnson</strong>. <p><strong>Source: </strong>Tohoku Mathematical Journal, Volume 71, Number 2, 319--326.</p><p><strong>Abstract:</strong><br/>
We show explicitly that the compact flat Kähler manifold of complex dimension three with $D_8$ holonomy studied by Dekimpe, Halenda and Szczepanski ([5] p. 367) possesses the structure of a nonsingular projective variety. This corrects a previous statement by H. Lange in [9] that the holonomy group of a hyperelliptic threefold is necessarily abelian.
</p>projecteuclid.org/euclid.tmj/1561082601_20190620220336Thu, 20 Jun 2019 22:03 EDT