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Convex isoperimetric sets in the Heisenberg group

Roberto Monti·Matthieu Rickly
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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.

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Roberto Monti, Matthieu Rickly. 2006-07-26. Convex isoperimetric sets in the Heisenberg group. https://arxiv.org/abs/math/0607666

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