Mass-capacity inequalities for conformally flat manifolds with boundary

Abstract

In this paper we prove a mass-capacity inequality and a volumetric Penrose inequality for conformally flat manifolds, in arbitrary dimensions. As a by-product of the proofs, Pólya-Szegö and Aleksandrov-Fenchel inequalities for mean-convex Euclidean domains are obtained. For each inequality, the case of equality is characterized.

final version; appeared in Comm PDE

References in corpus (2)

• On The Capacity of Surfaces in Manifolds with Nonnegative Scalar Curvature
• A volumetric Penrose inequality for conformally flat manifolds

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• A Penrose-type inequality for static spacetimes