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

Simon Brendle, Pei Ken Hung, Mu Tao Wang

Research output: Contribution to journalArticlepeer-review

49 Scopus citations

Abstract

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].

Original languageEnglish (US)
Pages (from-to)124-144
Number of pages21
JournalCommunications on Pure and Applied Mathematics
Volume69
Issue number1
DOIs
StatePublished - Jan 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2014 Wiley Periodicals, Inc.

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