Levi Lopes de Lima, Frederico Girão
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 $\gamma\geq 1$, 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 exotic black holes.
View original:
http://arxiv.org/abs/1304.7887
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