2006/07/26 by Roberto Monti, Monti, Roberto, Matthieu Rickly +1
Mathematics · #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #math.CA #math.DG
paper · pdf · doi:10.48550/arxiv.math/0607666
arxiv created 2006/07/26 · arxiv updated 2009/12/01
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.