A Penrose inequality for asymptotically locally hyperbolic graphs

Levi Lopes de Lima; Frederico Girão

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arXiv · 1304.7887

A Penrose inequality for asymptotically locally hyperbolic graphs

Levi Lopes de Lima·Frederico Girão

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Abstract

We use the inverse mean curvature flow to prove a sharp Alexandrov-Fenchel-type inequality for a class of hypersurfaces in certain locally hyperbolic manifolds. As an application we derive an optimal Penrose inequality for asymptotically locally hyperbolic graphs in any dimension $n\geq 3$. When the horizon has the topology of a compact surface of genus at least one, this provides an affirmative answer, for this class of initial data sets, to a question posed by Gibbons, Chru\'sciel and Simon on the validity of a Penrose-type inequality for black hole solutions carrying a higher genus horizon.

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Levi Lopes de Lima, Frederico Girão. 2013-04-30. A Penrose inequality for asymptotically locally hyperbolic graphs. https://arxiv.org/abs/1304.7887

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