The Riemannian Penrose inequality for asymptotically flat manifolds with non-compact boundary

Abstract

We prove the Riemannian Penrose inequality for asymptotically flat manifolds with non-compact boundary whose asymptotic region is modeled on a half-space. To this end, we develop the theory of weak free boundary inverse mean curvature flow further and establish the monotonicity of a modified Hawking mass along this flow. Our result also implies a non-optimal Penrose inequality for asymptotically flat support surfaces in $\mathbb{R}^3$ conjectured by G. Huisken.