标题：几何分析与相对论
图书信息
  作者：Hubert L.Bray (作者), William P.M (作者), 布雷(Hubert L.Bray) (编者), 米尼克兹(William P.Minicozzi) (编者) 出版社: 高等教育出版社; 第1版 (2011年6月1日) 
外文书名: Surveys in Geometric Analysis and Relativity 
精装: 546页 
正文语种: 英语 
开本: 16 
ISBN: 9787040327328 
条形码: 9787040327328 
产品尺寸及重量: 24.2 x 16.2 x 2.8 cm ; 1.2 Kg
内容简介
《几何分析与相对论》介绍了：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。 
作者简介
编者：（美国）布雷（Hubert L.Bray） （美国）米尼克兹（William P.Minicozzi） 
目录
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
Rradial 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 birkhoff: a closed geodesic on a two sphere
5 curve shortening flow
6 minimal surfaces
7 classification of embedded minimal surfaces
8 mean curvature flow
9 width and mean curvature flow
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 differentiability theorem of gromov-schoen
georgios daskalopoulos, chikako mese
1 introduction
2 definitions
3 main theorem
references
minimal surface techniques in riemannian geometry
a ilana 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 
references
……