A Minkowski Inequality for Hypersurfaces in the Anti‐de Sitter‐Schwarzschild Manifold |
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Authors: | Simon Brendle Pei‐Ken Hung Mu‐Tao Wang |
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Institution: | 1. Department of Mathematics, Stanford University, Stanford, CA, USA;2. Department of Mathematics, Columbia University, New York, NY, USA |
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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].© 2015 Wiley Periodicals, Inc. |
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