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(3 Sep 2012) Key: citeulike:11202378
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We use the inverse mean curvature flow to prove a sharp Alexandrov-Fenchel-type inequality for star-shaped, strictly mean convex hypersurfaces in hyperbolic $n$-space, $n≥ 3$. As an application, we establish an optimal Penrose inequality for asymptotically hyperbolic graphs carrying a minimal horizon, with the equality occurring if and only if the graph is an anti-de Sitter-Schwarzschild solution.
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