Mass-capacity inequalities for conformally flat manifolds with boundary

Details Mass-capacity inequalities for conformally flat manifolds with boundary Mass-capacity inequalities for conformally flat manifolds with boundary

2011-07-07

arxiv.org/abs/1107.1407v2

Mathematics

Differential Geometry

15 pages; v2: Euclidean statements strengthened

Scientific paper

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, capacity and Aleksandrov-Fenchel inequalities for
mean-convex Euclidean domains are obtained. For each inequality, the case of
equality is characterized.

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