A Minkowski Inequality for Hypersurfaces in the Anti‐de Sitter‐Schwarzschild Manifold | Zendy

Brendle Simon | Zendy; Hung PeiKen | Zendy; Wang MuTao | Zendy

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

Author(s) -

Brendle Simon,

Hung PeiKen,

Wang MuTao

Publication year - 2016

Publication title -

communications on pure and applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.12

H-Index - 115

eISSN - 1097-0312

pISSN - 0010-3640

DOI - 10.1002/cpa.21556

Subject(s) - mathematics , minkowski space , manifold (fluid mechanics) , schwarzschild radius , pure mathematics , minkowski inequality , de sitter universe , mean curvature flow , inequality , mathematical analysis , inverse , isoperimetric inequality , hölder's inequality , mean curvature , mathematical physics , curvature , geometry , classical mechanics , linear inequality , universe , physics , mechanical engineering , gravitation , astrophysics , engineering

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.

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