%0 Journal Article
%T Regularity of $C^1$ surfaces with prescribed mean curvature in three-dimensional contact sub-Riemannian manifolds
%A Matteo Galli
%A Manuel Ritor¨¦
%J Mathematics
%D 2015
%I arXiv
%X In this paper we consider surfaces of class $C^1$ with continuous prescribed mean curvature in a three-dimensional contact sub-Riemannian manifold and prove that their characteristic curves are of class $C^2$. This regularity result also holds for critical points of the sub-Riemannian perimeter under a volume constraint. All results are valid in the first Heisenberg group $\mathbb{H}^1$.
%U http://arxiv.org/abs/1501.07246v3