Convex isoperimetric sets in the Heisenberg group

Monti, Roberto; Rickly, Matthieu

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 2, pp. 391-415.

We characterize convex isoperimetric sets in the Heisenberg group. We first prove Sobolev regularity for a certain class of ${ℝ}^2$-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-Carathéodory distance.

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