Convex isoperimetric sets in the Heisenberg group

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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.

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Differential Geometry, Classical Analysis and ODEs

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http://salesiana.dossiersoluciones.com/handle/123456789/115140

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0607666
 http://arxiv.org/abs/math/0607666

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arXiv