Isoperimetric inequalities in conically bounded convex bodies
Differential Geometry
2014-10-15 v2
Abstract
In this paper we consider the problem of minimizing the relative perimeter under a volume constraint in the interior of a conically bounded convex set, i.e., an unbounded convex body admitting an \emph{exterior} asymptotic cone. Results concerning existence of isoperimetric regions, the behavior of the isoperimetric profile for large volumes, and a characterization of isoperimetric regions of large volume in conically bounded convex sets of revolution is obtained.
Cite
@article{arxiv.1404.0370,
title = {Isoperimetric inequalities in conically bounded convex bodies},
author = {Manuel Ritoré and Efstratios Vernadakis},
journal= {arXiv preprint arXiv:1404.0370},
year = {2014}
}
Comments
23 pages. Final version to appear in J. Geom. Anal