幾何分析與相對論

出版時(shí)間:2011-6  出版社:高等教育出版社  作者:(美)布雷 等編  頁數(shù):546  
Tag標(biāo)簽:無  

內(nèi)容概要

  自從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(xué)習(xí)廣義相對論提供方法以及正確的框架,而廣義相對論激發(fā)富有挑戰(zhàn)性的各種問題。本書包含23篇幾何分析和廣義相對論各領(lǐng)域的綜述性文章,作者均為該領(lǐng)域的知名專家。幾何分析方面的內(nèi)容包括:Yamabe問題、平均曲率流、極小曲面、調(diào)和映照、Ricci流、膠合與分裂結(jié)構(gòu)、函數(shù)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(nèi)容包括:正質(zhì)量定理、Penrose不等式、標(biāo)量曲率及Einstein約束方程、準(zhǔn)局域質(zhì)量泛函、高維黑洞拓?fù)?、漸近雙曲流形的正質(zhì)量定理等。本書可供幾何分析或相對論領(lǐng)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)

書籍目錄

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
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 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
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 definitions 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 kahler case
4 quaternionic kahler 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
andre 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 kahler-einstein metrics
xiaofeng sun, $hing-tung yam
1 introduction
2 complex structures of kahler-einstein manifolds
3 deformation of kahler-einstein metrics
4 local trivialization of polarization bundles and deformation of
sections
5 curvature of l2 metrics on direct hnage 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 diffeomorphisms between complete noncompact
surfaces
tom y h wan
1 introduction
2 harmonic map theory of universal teichmiiller space
3 asymptotic behavior of open harmonic embedding from the complex
plane into hyperbolic plane
references
compactifications of complete riemannian manifolds and their
applications
xiaodong wang
1 introduction
2 the geometric compactification
3 the martin compactification
4 the busemann boundary
5 a comparison theorem
references
some aspects of weil-petersson geometry of teichmiiller
spaces
sumio yamada
1 introduction
2 harmonic maps into t and an application
3 finite rank properties of
4 coxeter-tits construction
5 weil-petersson geodesic completeness
6 weil-petersson geometry of the universal teichmfiller space
7 embeddings of the coxeter complex into ut
8 summary and open problems
references

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  •   非常好的一本書,里面介紹了幾何分析與相對論的一些最新進(jìn)展
  •   本書可以看看,雖然論文上有,但作者的總結(jié)或許有一些好的思想可以借鑒.
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