几何分析进展
2011-11
高等教育
(波)简思科//李俊//(越南)冯
342
本书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。本书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。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。
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
