幾何分析進(jìn)展

內(nèi)容概要

　　本書介紹了幾何和理論物理領(lǐng)域一些重要的最新進(jìn)展，內(nèi)容包括MORge—AmPere方程，Kahler—Ricci流，完全非線性橢圓型和拋物型方程，K~ihler幾何中的典范度量，廣義相對(duì)論中的擬局部質(zhì)量概念等。本書深入地分析了基本的幾何對(duì)象和相關(guān)問(wèn)題，如Calabi—Yau流形及它們的Kahler—R．CC．流和度量性質(zhì)；介紹了適用于Monge—Ampere方程的有效且完備的法；用非線性橢圓型方程的奇異解與Einsteiiq方程的時(shí)間周期解討論了Yang—MillS聯(lián)絡(luò)的性質(zhì)；最后還討論了微分幾何及代數(shù)幾何的辛結(jié)構(gòu)。本書的每篇文章都是由該領(lǐng)域知名專家撰寫，可供微分幾何、代數(shù)幾何、辛幾何、理論物理等相關(guān)領(lǐng)域的研究人員參考。

書籍目錄

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

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