Capacity inequalities and rigidity of cornered/conical manifolds
Differential Geometry
2018-08-31 v2 Analysis of PDEs
Abstract
We prove capacity inequalities involving the total mean curvature of hypersurfaces with boundary in convex cones and the mass of asymptotically flat manifolds with non-compact boundary. We then give the analogous of P\"olia-Szeg\"o, Alexandrov-Fenchel and Penrose type inequalities in this setting. Among the techniques used in this paper are the inverse mean curvature flow for hypersurfaces with boundary.
Keywords
Cite
@article{arxiv.1704.04306,
title = {Capacity inequalities and rigidity of cornered/conical manifolds},
author = {C. Tiarlos Cruz},
journal= {arXiv preprint arXiv:1704.04306},
year = {2018}
}
Comments
Revised version. 18 pages; comments are welcome