Some higher order isoperimetric inequalities via the method of optimal transport
Differential Geometry
2013-05-15 v1 Analysis of PDEs
Abstract
In this paper, we establish some sharp inequalities between the volume and the integral of the -th mean curvature for -convex domains in the Euclidean space. The results generalize the classical Alexandrov-Fenchel inequalities for convex domains. Our proof utilizes the method of optimal transportation.
Keywords
Cite
@article{arxiv.1305.3004,
title = {Some higher order isoperimetric inequalities via the method of optimal transport},
author = {Sun-Yung A. Chang and Yi Wang},
journal= {arXiv preprint arXiv:1305.3004},
year = {2013}
}
Comments
21 pages