几何分析进展

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

《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。