《几何分析进展(英文)》主要内容简介：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 signifi-cant 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 dis-cover the latest results of many cutting-edge fields in mathematics.

Welcoming Speech (Extended) by Friedrich HirzebruchSpeech of Thanks by Shing-Tung YauPrefacePart 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 PlanesPart 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 ManifoldsPart 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 ConnectionsPart 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