A Minkowski Inequality for Hypersurfaces in the Anti-de Sitter-Schwarzschild Manifold

被引：88

作者：

Brendle, Simon ^{[1
]}

Hung, Pei-Ken ^{[2
]}

Wang, Mu-Tao ^{[2
]}

机构：

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

[2] Columbia Univ, Dept Math, New York, NY 10027 USA

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2016年 / 69卷 / 01期

基金：

美国国家科学基金会;

关键词：

QUASI-LOCAL MASS; ASYMPTOTICALLY HYPERBOLIC MANIFOLDS; SCALAR CURVATURE RIGIDITY; MEAN-CURVATURE; RIEMANNIAN-MANIFOLDS; PENROSE INEQUALITY; SURFACES; SPACE; POSITIVITY; FLOW;

D O I：

10.1002/cpa.21556

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a sharp inequality for hypersurfaces in the n-dimensional anti-de Sitter-Schwarzschild manifold for general n >= 3. This inequality generalizes the classical Minkowski inequality for surfaces in the three-dimensional euclidean space and has a natural interpretation in terms of the Penrose inequality for collapsing null shells of dust. The proof relies on a new monotonicity formula for inverse mean curvature flow and uses a geometric inequality established by the first author in [3]. (C) 2014 Wiley Periodicals, Inc.

引用

页码：124 / 144

页数：21

共 27 条

[1] Scalar curvature rigidity for asymptotically locally hyperbolic manifolds [J].