Stanislaw Janeczko、李俊、Duong H. Phong合著的《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Monge-Ampere方程，Kahler-Ricci流，完全非线性椭圆型和抛物型方程，Kahler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-Ricci流和度量性质；介绍了适用于Monge-Ampere方程的有效且完备的方法；用非线性椭圆型方程的奇异解与Einstein、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。本书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。

《几何分析进展》简介：The launch of this Advanced Lectures in Mathematics series is aimed at keeping mathematicians informed of the latest developments in mathematics, as well as to aid in the learning of new mathematical topics by students all over the world. Each volume consists of either an expository monograph or a collection of significant introductions to important topics. This series emphasizes the history and sources of motivation for the topics under discussion, and also gives an overview of the current status of research in each particular field. These volumes are the first source to which people will turn in order to learn new subjects and to discover the latest results of many cutting-edge fields in mathematics.

《几何分析进展》由Stanislaw Janeczko、李俊、Duong H. Phong合著。

Welcoming Speech (Extended) by Friedrich Hirzebruch

Speech of Thanks by Shing-Tung Yau

Preface

Part I. Monge-Ampere Equations and Nonlinear Partial Differential Equations

 Zbigniew Btocki: On Geodesics in the Space of Kahler Metrics

 Udo Simon and Ruiwei Xu: Geometric Modelling Techniques for the

Solution of Certain Monge-Ampere Equations

 Ovidiu Savin: A Localization Property at the Boundary for

Monge-Ampere Equation

 Stawomir Dinew and Slawomir Kotodziej: Pluripotential Estimates on

Compact Hermitian Manifolds

 Duong H. Phong and Jacob Sturm: On Pointwise Gradient Estimates

for the Complex Monge-Ampere Equation

 Luis Caffarelli, Yah Yan Li and Louis Nirenberg: Some Remarks on

Singular Solutions of Nonlinear Elliptic Equations. II. Symmetry

and Mouotonicity via Moving Planes

Part II. Canonical Metrics in Kahler Geometry

 Simon K. Donaldson: Calabi-Yau Metrics on Kummer Surfaces as a Model

Gluing Problem

 Jian Song and Yuan Yuan: The Kahler-Ricci Flow on Singular Calabi-Yau

Varieties

 Valentino Tosatti: The K-energy on Small Deformations of Constant Scalar

Curvature Kahler Manifolds

Part III. General Relativity and Yang-Mills Theory

 De-Xing Kong and Kefeng Liu: Time-periodic Solutions of the Einstein

Field Equations

 Mu-Tao Wang: Quantitative Properties of the New Quasilocal Mass

 Mike Scherfner, Simon Weiss and Shing-Tung Yau: A Review of the

Chern 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 Factorizations

from SYZ Transformations

 Dominic Joyce: On Manifolds with Corners

 Goo Ishikawa and Stanistaw Janeczko: Symplectic Invariants of

Parametric Singularities

 Fabrizio Catanese: Irreducibility of the Space of Cyclic Covers of

Algebraic Curves of Fixed Numerical Type and the Irreducible

Components of Sing(fling)

 Meirav Amram, David Garber, Robert Shwartz and Mina Teicher:

8-point -- Regenerations and Applications