Calculus of Variations and Geometric Measure Theory

M. Galli - M. Ritoré

Regularity of $C^1$ surfaces with prescribed mean curvature in three-dimensional contact sub-Riemannian manifolds

created by galli on 28 Jan 2015
modified on 01 May 2015

[BibTeX]

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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