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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