Isoperimetric Regions in Nonpositively Curved Manifolds
Differential Geometry
2016-04-12 v1
Abstract
Isoperimetric regions minimize the size of their boundaries among all regions with the same volume. In Euclidean and Hyperbolic space, isoperimetric regions are round balls. We show that isoperimetric regions in two and three-dimensional nonpositively curved manifolds are not necessarily balls, and need not even be connected.
Keywords
Cite
@article{arxiv.1604.02768,
title = {Isoperimetric Regions in Nonpositively Curved Manifolds},
author = {Joel Hass},
journal= {arXiv preprint arXiv:1604.02768},
year = {2016}
}