1209.0438 (Levi Lopes de Lima et al.)

An Alexandrov-Fenchel-type inequality in hyperbolic space with an
application to a Penrose inequality    [PDF]

Levi Lopes de Lima, Frederico Girão

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, $n\geq 3$. 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.

View original: http://arxiv.org/abs/1209.0438