Existence and Uniqueness of Constant Mean Curvature Foliation of Asymptotically Hyperbolic 3-Manifolds

被引：16

作者：

Neves, Andre ^{[1
]}

Tian, Gang ^{[1
]}

机构：

[1] Princeton Univ, Princeton, NJ 08544 USA

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2009年 / 19卷 / 03期

基金：

美国国家科学基金会;

关键词：

Foliations; constant mean curvature; SCALAR CURVATURE; MANIFOLDS; MASS; SOBOLEV;

D O I：

10.1007/s00039-009-0019-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove existence and uniqueness of foliations by stable spheres with constant mean curvature for 3-manifolds which are asymptotic to anti-de Sitter-Schwarzschild metrics with positive mass. These metrics arise naturally as spacelike timeslices for solutions of the Einstein equation with a negative cosmological constant.

引用

页码：910 / 942

页数：33

共 18 条

[1] BEST CONSTANTS IN INCLUSION THEOREM OF SOBOLEV AND NONLINEAR THEOREM OF FREDHOLM FOR CONFORMAL TRANSFORMATION OF SCALAR CURVATURE [J].