M. Galli - M. Ritoré
Regularity of $C^1$ surfaces with prescribed mean curvature in three-dimensional contact sub-Riemannian manifolds
Accepted Paper
Inserted: 28 jan 2015
Last Updated: 1 may 2015
Journal: Calc. Var. PDE
Year: 2015
Abstract:
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 $\mathbb{H}^1$.
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