**Author**: Li Xiuzhen et al

**Language**: English

**ISBN/ISSN**: 9787040252880

**Published on:** 2008-01

Hardcover

Geometric Analysis combines differentiae equations and differential geometry．An important aspect is to solve geometric problems by studying differentiae equations．Besides some known linear differential operators such as the Laplace operator, many differential equations arising from differential geometry are nonlinear．Particularly important example is the Monge-Amp~re 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 t0 be referred by graduate students and researchers in related areas．

Numerical Approximations to Extremal Metrics on Toric Surfaces .

R. S. Bunch, Simon K. Donaldson

1 Introduction

2 The set-up

3 Numerical algorithms: balanced metrics and refined approximations

4 Numerical results

5 Conclusions

References

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

Simon K. Donaldson

Introduction

1 Background

2 Toric manifolds

3 Toric Fano manifolds

4 Variants of toric differential geometry

5 The Mukai-Umemura manifold and its deformations

References

Gluing Constructions of Special Lagrangian Cones

Mark Haskins, Nikolaos Kapouleas

I Introduction

……