Convex isoperimetric sets in the Heisenberg group
Differential Geometry
2007-05-23 v1 Classical Analysis and ODEs
Abstract
We characterize convex isoperimetric sets in the Heisenberg group endowed with horizontal perimeter. We first prove Sobolev regularity for a certain class of vector fields in the plane with bounded variation, related to the curvature equations. Then, by an approximation-reparameterization argument, we show that the boundary of convex isoperimetric sets is foliated by geodesics of the Carnot-Caratheodory distance.
Cite
@article{arxiv.math/0607666,
title = {Convex isoperimetric sets in the Heisenberg group},
author = {Roberto Monti and Matthieu Rickly},
journal= {arXiv preprint arXiv:math/0607666},
year = {2007}
}