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几何分析与相对论

样章
作者：
Hubert L. Bray
定价：
98.00元
ISBN：
978-7-04-032732-8
版面字数：
580.000千字
开本：
16开
全书页数：
546页
装帧形式：
精装
重点项目：
暂无
出版时间：
2011-06-14
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
几何分析

自从爱因斯坦提出广义相对论以来，微分几何就与广义相对论密不可分。微分几何和几何分析为学习广义相对论提供方法以及正确的框架，而广义相对论激发富有挑 战性的各种问题。《几何分析与相对论》包含23篇几何分析和广义相对论各领域的综述性文章，作者均为该领域的知名专家。几何分析方面的内容包括 Yamabe问题、平均曲率流、极小曲面、调和映照、Ricci流、胶合与分裂结构、函数论、流形的塌陷、Kahler-Einstein度量、完备流形 的渐近几何以及Teichmuller空间几何等。广义相对论方面的内容包括正质量定理、Penrose不等式、标量曲率及Einstein约束方程、准 局域质量泛函、高维黑洞拓扑、渐近双曲流形的正质量定理等。《几何分析与相对论》可供几何分析或相对论领域的研究人员和研究生参考。

  • 前辅文
  • On the Positive Mass, Penrose, and ZAS Inequalities in General Dimension Hubert L Bray
    • 1 Dedication
    • 2 Introduction
    • 3 A Trio of Inequalities
    • References
  • Recent Progress on the Yamabe Problem Simon Brendle, Fernando C Marques
    • 1 The Yamabe Problem
    • 2 The Compactness Conjecture
    • 3 Non-compactness Results in Dimension n ¸ 25
    • 4 A Compactness Result in Dimension n • 24
    • 5 The Parabolic Yamabe Flow
    • References
  • Some Recent Progress on Mean Curvature Flow for Entire Lagrangian Graphs Jingyi Chen
    • 1 Introduction
    • 2 Longtime Existence With Lipschitz Continuous Initial Data
    • 3 Uniqueness and Viscosity Solutions
    • 4 Self-similar Solutions
    • References
  • Radial Viewpoint on Minimal Surfaces Jaigyoung Choe
    • 1 Introduction
    • 2 Cone
    • 3 Horizon
    • 4 Non-Euclidean Space
    • 5 Ray preserving Metric
    • 6 Varying Curvature
    • 7 Embeddedness
    • References
  • Minimal Surfaces and Mean Curvature Flow Tobias H Colding, William P Minicozzi II
    • 1 Introduction
    • 2 Harmonic Functions and the Heat Equation
    • 3 Energy of a Curve
    • 4 Birkho®: A Closed Geodesic on a Two Sphere
    • 5 Curve Shortening Flow
    • 6 Minimal Surfaces
    • 7 Classi¯cation of Embedded Minimal Surfaces
    • 8 Mean Curvature Flow
    • 9 Width and mean curvature °ow
    • 10 Singularities for MCF
    • 11 Smooth Compactness Theorem for Self-shrinkers
    • 12 The Entropy
    • 13 An Application
    • 14 Non-compact self-shrinkers
    • References
  • Scalar Curvature and the Einstein Constraint Equations Justin Corvino, Daniel Pollack
    • 1 Introduction
    • 2 The Constraint Equations
    • 3 A Tour of Asymptotically Flat Solutions
    • 4 The Conformal Method
    • 5 Gluing Constructions
    • References
  • On the Intrinsic Di®erentiability Theorem of Gromov-Schoen Georgios Daskalopoulos, Chikako Mese
    • 1 Introduction
    • 2 De¯nitions
    • 3 Main Theorem
    • References
  • Minimal Surface Techniques in Riemannian Geometry Ailana Fraser
    • 1 Introduction
    • 2 Brief Overview of Some Geodesic Methods
    • 3 Existence of Minimal Surfaces
    • 4 Second Variation Theory for Minimal Surfaces and Applications
    • References
  • Stability and Rigidity of Extremal Surfaces in Riemannian Geometry and General Relativity Gregory J Galloway
    • 1 Minimal Hypersurfaces in Manifolds of Nonnegative
    • Scalar Curvature
    • 2 Marginally Outer Trapped Surfaces
    • 3 Positivity of Mass for Asymptotically Hyperbolic Manifolds
    • References
  • Convex Hypersurfaces of Constant Curvature in Hyperbolic Space Bo Guan, Joel Spruck
    • 1 Introduction
    • 2 Formulas on Hypersurfaces
    • 3 The Asymptotic Angle Maximum Principle and
    • Gradient Estimates
    • 4 Curvature Estimates
    • 5 Uniqueness and Foliations
    • References
  • Ricci Flow in Two Dimensions James Isenberg, Rafe Mazzeo, Natasa Sesum
    • 1 Introduction
    • 2 General Considerations
    • 3 Compact Surfaces
    • 4 Open Surfaces
    • 5 Flows on Incomplete Surfaces
    • References
  • Doubling and Desingularization Constructions for Minimal Surfaces Nikolaos Kapouleas
    • 1 Introduction
    • 2 Doubling Constructions
    • 3 Desingularization Constructions
    • 4 Minimal Surfaces in the Round Three-Sphere
    • 5 The Building Blocks for the Desingularization Construction
    • 6 An Initial Surface for the Desingularization Construction
    • 7 The Family of Initial Surfaces for the
    • Desingularization Construction
    • 8 Main Estimates and Outline of the Proof
    • References
  • The Metric Properties of Lagrangians Yng-Ing Lee
    • 1 Introduction
    • 2 A Short Survey
    • 3 De¯nitions and Properties
    • 4 Singularities and Geometric Measure Theory
    • 5 Gluing and Singular Perturbation
    • References
  • Structure of Complete Manifolds with Positive Spectrum Peter Li
    • 1 Introduction
    • 2 Riemannian Case
    • 3 KÄahler Case
    • 4 Quaternionic KÄahler Manifolds, Cayley Manifolds, and Locally
    • Symmetric Spaces
    • 5 Manifolds of Finite Volume
    • 6 Further Generalizations
    • References
  • Topology of Sobolev Mappings and Associated Variational Problems Fang Hua Lin
    • Introduction
    • 1 Analytical and Topological Properties of Sobolev Maps
    • 2 Singularity of Energy Minimizing Maps
    • 3 Limits of Singular Sets of p-Energy Minimizing Maps
    • References
  • A Survey of Research on Boundary Behavior of Compact Manifolds via the Positive Mass Theorem Pengzi Miao
    • 1 Introduction
    • 2 Statement of the Positive Mass Theorem
    • 3 On compact Manifolds with Nonnegative Scalar Curvature
    • 4 On Compact Manifolds with Negative Scalar Curvature
    • References
  • Recent Progress on Singularities of Lagrangian Mean Curvature Flow Andr¶e Neves
    • 1 Introduction
    • 2 Preliminaries
    • 3 Basic Techniques
    • 4 Applications I: Blow-ups
    • 5 Applications II: Self-Expanders
    • 6 Application III: Stability of Singularities
    • 7 Open Questions
    • References
  • Geometric Structures of Collapsing Riemannian Manifolds I Aaron Naber, Gang Tian
    • 1 Introduction
    • 2 Structure of Collapsed Spaces
    • 3 Geometry of Toric Quotients
    • 4 Geometry of Toric Quotients II
    • 5 Proof of Theorems 11 and 12
    • 6 Proof of Theorem 13
    • A Geometry of Quotients
    • B Orbifolds
    • References
  • Deformation of KÄahler-Einstein Metrics Xiaofeng Sun, Shing-Tung Yau
    • 1 Introduction
    • 2 Complex Structures of KÄahler-Einstein Manifolds
    • 3 Deformation of KÄahler-Einstein Metrics
    • 4 Local Trivialization of Polarization Bundles and Deformation of Sections
    • 5 Curvature of L2 Metrics on Direct Image Sheaves
    • 6 Appendix
    • References
  • Reverse Bubbling in Geometric Flows
    • Peter M Topping
    • 1 Introduction
    • 2 The Harmonic map Flow
    • 3 Ricci Flow
    • 4 Addendum | Mean Curvature Flow
    • References
  • Review on Harmonic Di®eomorphisms Between Complete Noncompact Surfaces Tom Y H Wan
    • 1 Introduction
    • 2 Harmonic Map Theory of Universal TeichmÄuller Space
    • 3 Asymptotic Behavior of Open Harmonic Embedding From
    • the Complex Plane Into Hyperbolic Plane
    • References
  • Compacti¯cations of Complete Riemannian Manifolds and Their Applications Xiaodong Wang
    • 1 Introduction
    • 2 The Geometric Compacti¯cation
    • 3 The Martin Compacti¯cation
    • 4 The Busemann Boundary
    • 5 A Comparison Theorem
    • References
  • Some Aspects of Weil-Petersson Geometry of TeichmÄuller Spaces Sumio Yamada
    • 1 Introduction
    • 2 Harmonic Maps into T and an Application
    • 3 Finite Rank Properties of T
    • 4 Coxeter-Tits Construction
    • 5 Weil-Petersson Geodesic Completeness
    • 6 Weil-Petersson Geometry of the Universal TeichmÄuller Space
    • 7 Embeddings of the Coxeter Complex into UT
    • 8 Summary and Open Problems
    • References

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