A geometric capacitary inequality for sub-static manifolds with harmonic\n potentials

2020/12/18 by Virginia Agostiniani, Agostiniani, Virginia, Lorenzo Mazzieri +3 · 1 citation
Mathematics · Physics and Astronomy · #31C12 (Primary) 53C21 #83C57 (Secondary) #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2012.10164

openalex publication_date 2020/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that associated with a sub-static asymptotically flat\nmanifold endowed with a harmonic potential there is a one-parameter family\n F_\β of functions which are monotone along the level-set flow of the\npotential. Such monotonicity holds up to the optimal threshold\n\β=\(n-2)/(n-1) and allows us to prove a geometric capacitary\ninequality where the capacity of the horizon plays the same role as the ADM\nmass in the celebrated Riemannian Penrose Inequality.\n

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