Inserted: 26 jul 2006
Last Updated: 27 oct 2008
Journal: Ann. Scuola Norm. Sup. Pisa Cl. Sci.
We characterize convex isoperimetric sets in the Heisenberg group endowed with horizontal perimeter. 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, by an approximation-reparameterization argument, we show that the boundary of convex isoperimetric sets is foliated by geodesics of the Carnot-Carathéodory distance.