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