图书信息

内容简介

作者简介

目录

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

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