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.

Cited by in corpus (2)

• Nonlinear Isocapacitary Concepts of Mass in 3-Manifolds with Nonnegative Scalar Curvature
• A Note about Isotopy and Concordance of Positive Scalar Curvature Metrics on Compact Manifolds with Boundary