Osaka Journal of Mathematics

Numerical algorithm for finding balanced metrics

Yuji Sano

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The purpose of this paper is to give an explicit statement with respect to a numerical algorithm for finding balanced metrics, which has already been pointed out by Donaldson [3].

Article information

Osaka J. Math., Volume 43, Number 3 (2006), 679-688.

First available in Project Euclid: 25 September 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}
Secondary: 14C05: Parametrization (Chow and Hilbert schemes)


Sano, Yuji. Numerical algorithm for finding balanced metrics. Osaka J. Math. 43 (2006), no. 3, 679--688.

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  • T. Aubin: Réduction du cas positif de l'équation de Monge-Ampère sur les variétés kählériennes compactes á la démonstration d'une inéqalité, J. Funct. Anal. 57 (1984), 143--153.
  • S.K. Donaldson: Scalar curvature and projective embeddings, I, J. Diff. Geom. 59 (2001), 479--522.
  • S.K. Donaldson: Scalar curvature and projective embeddings, II, arXiv: math.DG/0407534.
  • A. Futaki: On a character of the automorphism group of a compact manifold, Invent. Math. 87 (1987), 655--660.
  • D. Gieseker: Geometric invariant theory and applications to moduli problems; in Invariant Theory (Montecatini, 1982), Lecture Notes in Math. 996, Springer, Berlin, 1983, 45--73.
  • H. Luo: Geometric criterion for Gieseker-Mumford stability of polarized manifolds, J. Diff. Geom. 49 (1998), 577--599.
  • T. Mabuchi: An energy-theoretic approach to the Hitchin-Kobayashi correspondence for manifolds, I, Invent. Math. 159 (2005), 225--243.
  • A. Nadel: Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature, Annals of Math. 132 (1990), 549--596.
  • D.H. Phong and J. Sturm: Stability, energy functionals, and Kähler-Einstein metrics, Comm. in Analysis and Geometry 11 (2003) 565--597.
  • Y. Sano: On stability criterion of complete intersections, J. Geom. Anal. 14 (2004), 533--544.
  • G. Tian: On Kähler-Einstein metrics on certain Kähler manifolds with $C_1(M)>0$, Invent. Math. 89 (1987) 225--246.
  • S. Zhang: Heights and reductions of semi-stable varieties, Compositio Math. 104 (1996), 77--105.