A Penrose inequality for asymptotically locally hyperbolic graphs

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 $n\ge 3$. 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, Chruściel and Simon on the validity of a Penrose-type inequality for black hole solutions carrying a higher genus horizon.

17 pages; the main results in this posting have been incorporated into (the published version of) arXiv:1209.0438

References in corpus (2)

• A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold
• The Gauss-Bonnet-Chern mass for graphic manifolds

Cited by in corpus (1)

• Penrose inequalities and a positive mass theorem for charged black holes in higher dimension