Brendle's inequality on static manifolds
arXiv:1603.00379 · doi:10.1007/s12220-017-9814-3
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 Chruściel and Simon \cite{CS}.