几何分析手册（第Ⅰ卷）
2008-8
高等教育出版社
季理真 等主编
676
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Moduli Spaces of Projective
ManifoldsGeometric Analysis combines differential equations and
differential geometry. An important aspect is to solve geometric
problems by studying differential equations.Besides some known
linear differential operators such as the Laplace operator,many
differential equations arising from differential geometry are
nonlinear. A particularly important example is the Monge-Ampre
equation. Applications to geometric problems have also motivated
new methods and techniques in differential equations. The field of
geometric analysis is broad and has had many striking applications.
This handbook of geometric analysis provides introductions to and
surveys of important topics in geometric analysis and their
applications to related fields which is intend to be referred by
graduate students and researchers in related areas.
Numerical Approximations to Extremal Metrics on Toric Surfaces
R. S. Bunch, Simon K. Donaldson I
1 Introduction
2 The set-up
2.1 Algebraic metrics
2.2 Decomposition of the curvature tensor
2.3 Integration
3 Numerical algorithms: balanced metrics and refined
approximations.
4 Numerical results
4.1 The hexagon
4.2 The pentagon
4.3 The octagon
4.4 The heptagon
5 Conclusions
References
Kiihler Geometry on Toric Manifolds, and some other Manifolds with
Large Symmetry
Glning 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
Stable Constant Mean Curvature Surfaces
A General Asymptotic Decay Lemma for Elliptic Problems
Uniformization of Open Nonnegatively Curved K／ihler Manifolds in
Higher Dimensions
Geometry of Measures：Harmonic Analysis Meets Geometric Measure
Theory
The Monge Ampere 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
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