Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces

Abstract

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 $n\ge 3$ an optimal Penrose inequality for certain graphs in hyperbolic space ${\mathbb{H}}^{n+1}$ whose boundary has constant mean curvature $n-1$.

18 pages, no figures

References in corpus (3)

• Rigidity and Positivity of Mass for Asymptotically Hyperbolic Manifolds
• Geometric invariance of mass-like asymptotic invariants
• Mass-capacity inequalities for conformally flat manifolds with boundary

Cited by in corpus (8)

• General Bounds on Holographic Complexity
• A rigidity result for the graph case of the Penrose inequality
• A new mass for asymptotically flat manifolds
• A Penrose inequality for asymptotically locally hyperbolic graphs
• The equality case of the Penrose inequality for asymptotically flat graphs
• Penrose inequalities and a positive mass theorem for charged black holes in higher dimension
• The GBC mass for asymptotically hyperbolic manifolds
• On the limiting behavior of the Brown-York quasi-local mass in asymptotically hyperbolic manifolds