圖書信息
外文書名: Surveys in Geometric Analysis and Relativity
精裝: 546頁
正文語種: 英語
開本: 16
ISBN: 9787040327328
條形碼: 9787040327328
產品尺寸及重量: 24.2 x 16.2 x 2.8 cm ; 1.2 Kg
內容簡介
《幾何分析與相對論》介紹了：愛因斯坦提出廣義相對論以來，微分幾何就與廣義相對論密不可分。微分幾何和幾何分析為學習廣義相對論提供方法以及正確的框架，而廣義相對論激發富有挑戰性的各種問題。《幾何分析與相對論》包含23篇幾何分析和廣義相對論各領域的綜述性文章，作者均為該領域的知名專家。幾何分析方面的內容包括：Yamabe問題、平均曲率流、極小曲面、調和映照、Ricci流、膠合與分裂結構、函式論、流形的塌陷、Kahler-Einstein度量、完備流形的漸近幾何以及Teichmuller空間幾何等。廣義相對論方面的內容包括：正質量定理、Penrose不等式、標量曲率及Einstein約束方程、準局域質量泛函、高維黑洞拓撲、漸近雙曲流形的正質量定理等。《幾何分析與相對論》可供幾何分析或相對論領域的研究人員和研究生參考。
作者簡介
編者：（美國）布雷（Hubert L.Bray） （美國）米尼克茲（William P.Minicozzi）
目錄
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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