Riemannian Penrose inequality via Nonlinear Potential Theory

Abstract

We provide a new proof of the Riemannian Penrose inequality for time-symmetric asymptotically flat initial data with a single black-hole horizon. The proof proceeds through a newly established monotonicity formula holding along the level sets of the $p$-capacitary potential of the horizon boundary, in any asymptotically flat $3$-manifold with nonnegative scalar curvature.