Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces

Details Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces

2012-01-24

arxiv.org/abs/1201.4991v1

Mathematics

Differential Geometry

18 pages, no figures

Scientific paper

We establish versions of the Positive Mass and Penrose inequalities for a
class of asymptotically hyperbolic hypersurfaces. In particular, under the
usual dominant energy condition, we prove in all dimensions $n\geq 3$ an
optimal Penrose inequality for certain graphs in hyperbolic space $\mathbb
H^{n+1}$ whose boundary has constant mean curvature $n-1$.

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