Fibred rational surfaces with a certain extremal property are classified.

It is shown that any horizontally conformal submersion of a CR-submanifold M of a Kaehler manifold $\overline{M}$ onto a Kaehler manifold N is a Riemannian submersion. Moreover, if M is mixed geodesic, then it is proved that such submersion is a harmonic map.

By utilizing Nevanlinna's value distribution theory, we find the meromorphic solutions of the functional equations of the type P(f)P(g) = 1, where P is a polynomial with three distinct zeros at least.

Let G be a discrete quasiconformal group preserving B³ whose limit set Λ(G) is purely conical and all of ∂B³. Let Ĝ be a non-elementary normal subgroup of G: we show that there exists a set $\mathscr{A}$ of full measure in Λ(G) so that $\mathscr{A}$, regarded as a subset of Λ (Ĝ), has "fat horospherical" dynamics relative to Ĝ. As an application we will bound from below the exponent of convergence of Ĝ in terms of the Hausdorff dimension of $\mathscr{A}$.

The author studies the quotient group $\mathscr{E}$(SO(4))/$\mathscr{E}$_#(SO(4)), where $\mathscr{E}$(SO(4)) is the group of homotopy classes of self homotopy equivalences of the rotation group SO(4) and $\mathscr{E}$_#(SO(4)) is the subgroup of it consisting of elements that induce the identity on homotopy groups.

The dilatation of a pseudo-Anosov braid is a conjugacy invariant. In this paper, we study the dilatation of a special family of pseudo-Anosov braids. We prove an inductive formula to compute their dilatation, a monotonicity and an asymptotic behavior of the dilatation for this family of braids. We also give an example of a family of pseudo-Anosov braids with arbitrarily small dilatation such that the mapping torus obtained from such braid has 2 cusps and has an arbitrarily large volume.

Let M be an n-dimensional complete minimal submanifold in R^n+p. Lei Ni proved that if M has sufficiently small total scalar curvature, then M has only one end. We improve the upper bound of total scalar curvature. We also prove that if M has the same upper bound of total scalar curvature, there is no nontrivial L² harmonic 1-form on M.

We give an explicit formula for the zeros of the Rankin type zeta-function by using the projection of the C^∞-automorphic forms introduced by Sturm (1981). Our theorem gives a correlation of the zeros of the L-functions and the Hecke eigenvalues.

In this paper, by using Ahlfors' theory of covering surface, the existence of T direction of meromorphic function concerning multiple values is obtained. Results are obtained extending the previous results due to Guo, Zheng, Ng in Bull. Austral. Math. Soc., 69 (2004), 277-287. Moreover, we give an affirmative answer to the question by Wang and Gao in Bull. Austral. Math. Soc., 75 (2007), 459-468.

This paper studies the uniqueness of meromorphic functions that share three values CM and obtain some results that are improvements and generalizations of that of H. Ueda, G. Brosch, etc.