Brendle's inequality on static manifolds

TL;DR

This paper extends Brendle's geometric inequality to static manifolds, providing bounds on mean curvature integrals and deriving a reverse Penrose inequality for static asymptotically hyperbolic manifolds.

Contribution

It generalizes Brendle's inequality to static manifolds and establishes a reverse Penrose inequality in this broader context.

Findings

Bound on inverse mean curvature integral by horizon data

Reverse Penrose inequality on static asymptotically hyperbolic manifolds

Extension of geometric inequalities to static manifold setting

Abstract

We generalize Brendle's geometric inequality considered in \cite{B} to static manifolds. The inequality bounds the integral of inverse mean curvature of an embedded mean-convex hypersurface by geometric data of the horizon. As a consequence, we obtain a reverse Penrose inequality on static asymptotically locally hyperbolic manifolds in the spirit of Chru\'{s}ciel and Simon \cite{CS}.