Kähler Geometry on Toric Manifolds, and some other Manifolds with Large Symmetry

Handbook of Geometric Analysis 作者：Lizhen Ji　　 ISBN：978-7-04-025288-0　出版时间：2008-08-15

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目录

前辅文

Numerical Approximations to Extremal Metrics on Toric Surfaces

Kähler Geometry on Toric Manifolds, and some other Manifolds with Large Symmetry

Gluing Constructions of Special Lagrangian Cones

Harmonic Mappings

Harmonic Functions on Complete Riemannian Manifolds

Complexity of Solutions of Partial Differential Equations

Variational Principles on Triangulated Surfaces

Asymptotic Structures in the Geometry of Stability and Extremal Metrics Toshiki Mabuchi

Stable Constant Mean Curvature Surfaces

A General Asymptotic Decay Lemma for Elliptic Problems

Uniformization of Open Nonnegatively Curved Kähler Manifolds in Higher Dimensions

Geometry of Measures: Harmonic Analysis Meets Geometric Measure Theory Tatiana. Toro

The Monge-Ampère Eequation and its Geometric Aapplications

Lectures on Mean Curvature Flows in Higher Codimensions

Local and Global Analysis of Eigenfunctions on Riemannian Manifolds

Yau's Form of Schwarz Lemma and Arakelov Inequality On Moduli Spaces of Projective Manifolds
- Simon K. Donaldson
- Introduction
- 1 Background
- 1.1 Gauge theory and holomorphic bundles
- 1.2 Symplectic and complex structures
- 1.3 The equations
- 2 Toric manifolds
- 2.1 Local differential geometry
- 2.2 The global structure
- 2.3 Algebraic metrics and asymptotics
- 2.4 Extremal metrics on toric varieties
- 3 Toric Fano manifolds
- 3.1 The Kähler-Ricci soliton equation
- 3.2 Continuity method, convexity and a fundamental inequality
- 3.3 A priori estimate
- 3.4 The method of Wang and Zhu
- 4 Variants of toric differential geometry
- 4.1 Multiplicity-free manifolds
- 4.2 Manifolds with a dense orbit
- 5 The Mukai-Umemura manifold and its deformations
- 5.1 Mukai's construction
- 5.2 Topological and symplectic picture
- 5.3 Deformations
- 5.4 The α-invariant
- References

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