Mass-capacity inequalities for conformally flat manifolds with boundary
Differential Geometry
2014-03-25 v3 General Relativity and Quantum Cosmology
Analysis of PDEs
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, P\'olya-Szeg\"o and Aleksandrov-Fenchel inequalities for mean-convex Euclidean domains are obtained. For each inequality, the case of equality is characterized.
Keywords
Cite
@article{arxiv.1107.1407,
title = {Mass-capacity inequalities for conformally flat manifolds with boundary},
author = {Alexandre Freire and Fernando Schwartz},
journal= {arXiv preprint arXiv:1107.1407},
year = {2014}
}
Comments
final version; appeared in Comm PDE