We characterize convex isoperimetric sets in the Heisenberg group. We first prove Sobolev regularity for a certain class of R2 -valued vector fields of bounded variation in the plane related to the curvature equations. Then we show that the boundary of convex isoperimetric sets is foliated by geodesics of the Carnot-Caratheodory distance.

Convex isoperimetric sets in the Heisenberg group

MONTI, ROBERTO;
2009

Abstract

We characterize convex isoperimetric sets in the Heisenberg group. We first prove Sobolev regularity for a certain class of R2 -valued vector fields of bounded variation in the plane related to the curvature equations. Then we show that the boundary of convex isoperimetric sets is foliated by geodesics of the Carnot-Caratheodory distance.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/147173
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