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

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 in...

Full description

Saved in:
Bibliographic Details
Published inCommunications on pure and applied mathematics Vol. 69; no. 1; pp. 124 - 144
Main Authors Brendle, Simon, Hung, Pei-Ken, Wang, Mu-Tao
Format Journal Article
LanguageEnglish
Published New York Blackwell Publishing Ltd 01.01.2016
John Wiley and Sons, Limited
Subjects
Applied mathematics
Euclidean space
Geometry
Online AccessGet full text

Cover

More Information
Summary: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].© 2015 Wiley Periodicals, Inc.
Bibliography:ark:/67375/WNG-XZ4626XW-J
istex:115CCDC599487E06FBAF5231BD28CCF8DC4D0516
ArticleID:CPA21556
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.21556