Riemannian Penrose inequality via Nonlinear Potential Theory

2022/05/23 by Virginia Agostiniani, Agostiniani, Virginia, Carlo Mantegazza +5
Engineering · Mathematics · Physics and Astronomy · #31C12 #31C15 #53C21 #53Z05 #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2205.11642

openalex publication_date 2022/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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