几何分析与相对论

stability of singularities7 open questionsreferencesgeometric structures of collapsing riemannian manifolds iaaron naber, gang tian1 introduction2 structure of collapsed spaces3 geometry of toric quotients4 geometry of toric quotients ii5 proof of theorems 11 and 126 proof of theorem 13a geometry of quotientsb orbifoldsreferencesdeformation of kahler-einstein metricsxiaofeng sun, $hing-tung yam1 introduction2 complex structures of kahler-einstein manifolds3 deformation of kahler-einstein metrics4 local trivialization of polarization bundles and deformation ofsections5 curvature of l2 metrics on direct hnage sheaves6 appendixreferencesreverse bubbling in geometric flowspeter m topping1 introduction2 the harmonic map flow3 ricci flow4 addendum -- mean curvature flowreferencesreview on harmonic diffeomorphisms between complete noncompactsurfacestom y h wan1 introduction2 harmonic map theory of universal teichmiiller space3 asymptotic behavior of open harmonic embedding from the complexplane into hyperbolic planereferencescompactifications of complete riemannian manifolds and theirapplicationsxiaodong wang1 introduction2 the geometric compactification3 the martin compactification4 the busemann boundary5 a comparison theoremreferencessome aspects of weil-petersson geometry of teichmiillerspacessumio yamada1 introduction2 harmonic maps into t and an application3 finite rank properties of4 coxeter-tits construction5 weil-petersson geodesic completeness6 weil-petersson geometry of the universal teichmfiller space7 embeddings of the coxeter complex into ut8 summary and open problemsreferences

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。本书包含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。本书可供几何分析或相对论领域的研究人员和研究生参考。