Convex isoperimetric sets in the Heisenberg group

Details Convex isoperimetric sets in the Heisenberg group Convex isoperimetric sets in the Heisenberg group

2006-07-26

arxiv.org/abs/math/0607666v1

Mathematics

Differential Geometry

Scientific paper

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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