A Volume Comparison Theorem for Asymptotically Hyperbolic Manifolds

被引：20

作者：

Brendle, Simon ^{[1
]}

Chodosh, Otis ^{[1
]}

机构：

[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2014年 / 332卷 / 02期

基金：

美国国家科学基金会;

关键词：

RIEMANNIAN PENROSE INEQUALITY; MEAN-CURVATURE FLOW; SCALAR CURVATURE; SURFACES; MASS;

D O I：

10.1007/s00220-014-2074-1

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We define a notion of renormalized volume of an asymptotically hyperbolic manifold. Moreover, we prove a sharp volume comparison theorem for metrics with scalar curvature at least -6. Finally, we show that the inequality is strict unless the metric is isometric to one of the Anti-deSitter-Schwarzschild metrics.

引用

页码：839 / 846

页数：8

共 13 条

[1]

Bray H., 1997, THESIS STANDFORD U

[2]

Bray HL, 2001, J DIFFER GEOM, V59, P177

[3] On the capacity of surfaces in manifolds with nonnegative scalar curvature [J].