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arXiv · 1209.0669

A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold

Simon Brendle·Pei-Ken Hung·Mu-Tao Wang
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Abstract

We prove a sharp inequality for hypersurfaces in the n-dimensional Anti-deSitter-Schwarzschild manifold for general n greater or equal to 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].

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Simon Brendle, Pei-Ken Hung, Mu-Tao Wang. 2014-07-21. A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold. https://arxiv.org/abs/1209.0669

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