几何分析进展

出版时间： 2011

内容简介
　　《几何分析进展》介绍了几何和理论物理领域一些重要的最新进展，内容包括MORge—AmPere方程，Kahler—Ricci流，完全非线性椭圆型和拋物型方程，K~ihler几何中的典范度量，广义相对论中的拟局部质量概念等。《几何分析进展》深入地分析了基本的几何对象和相关问题，如Calabi—Yau流形及它们的Kahler—R．CC．流和度量性质；介绍了适用于Monge—Ampere方程的有效且完备的法；用非线性椭圆型方程的奇异解与Einsteiiq方程的时间周期解讨论了Yang—MillS联络的性质；最后还讨论了微分几何及代数几何的辛结构。《几何分析进展》的每篇文章都是由该领域知名专家撰写，可供微分几何、代数几何、辛几何、理论物理等相关领域的研究人员参考。

Welcoming Speech （Extended） by lriedrich Hirzebruch
Speech of Thanks by Shing-Tung Yau
Preface
Part I. Monge-Ampre Equations and Nonlinear PartialDifferential Equations
Zbigniew Btocki： On Geodesics in the Space of K/hler Metrics
Udo Simon and Ruiwei Xu： Geometric Modelling Techniques for theSolution of Certain Monge-Ampre Equations
Ovidiu Savin： A Localization Property at the Boundary forMonge-Ampre Equation
Stawomir Dinew and Stawomir Kotodziej： PluripotentiM Estimates onCompact Hermitian Manifolds
Duong H. Phong and Jacob Sturm： On Pointwise Gradient Estimatesfor the Complex Monge-Ampre Equation
Luis Caffarelli， Yah Yah Li and Louis Nirenberg： Some Remarks onSingular Solutions of Nonlinear Elliptic Equations. II. Symmetryand Monotonicity via Moving Planes
Part II. Canonical Metrics in Kihler Geometry
Simon K. Donaldson： Calabi-Yau Metrics on Kummer Surfaces as a ModelGluing Problem
Jian Song and Yuan Yuan： The Khler-Ricci Flow on Singular Calabi-YauVarieties
Valentino Tosatti： The K-energy on Small Deformations of Constant ScalarCurvature Khler Manifolds
Part III. General Relativity and Yang-Mills Theory
De-Xing Kong and Kefeng Liu： Time-periodic Solutions of the EinsteinField Equations
Mu-Tao Wang： Quantitative Properties of the New Quasilocal Mass
Mike Scherfner， Simon Weiss and Shing-Tung Yau： A Review of theChern Conjecture for Isoparametric Hypersurfaces in Spheres
Mark Stern： Geometry of Stable Yang-Mills Connections
Part IV. Algebraic and Symplectic Methods
Kwokwai Chan and Naichung Conan Leung： Matrix Factorizationsfrom SYZ Transformations
Dominic Joyce： On Manifolds with Corners
Goo Ishikawa and Stanistaw Janeczko： Symplectic Invariants ofParametric Singularities
Fabrizio Catanese： Irreducibility of the Space of Cyclic Covers ofAlgebraic Curves of Fixed Numerical Type and the IrreducibleComponents of Sing（92；tg）
Meirav Amram， David Garber， Robert Shwartz and Mina Teicher：8-point -- Regenerations and Applications