The regularity of Euclidean Lipschitz boundaries with prescribed mean curvature in three-dimensional contact sub-Riemannian manifolds

TL;DR

This paper proves that in three-dimensional contact sub-Riemannian manifolds, sets with prescribed mean curvature and Euclidean Lipschitz boundaries have characteristic curves of class C^2 when locally represented as regular intrinsic graphs, improving previous results.

Contribution

It establishes higher regularity of characteristic curves for sets with prescribed mean curvature in a sub-Riemannian setting, under local regularity assumptions.

Findings

Characteristic curves are of class C^2 under given conditions.

Results improve previous regularity theorems.

Provides new insights into geometric measure theory in sub-Riemannian manifolds.

Abstract

In this paper we consider a set $E\subset\Omega$ with prescribed mean curvature $f\in C(\Omega)$ and Euclidean Lipschitz boundary $\partial E=\Sigma$ inside a three-dimensional contact sub-Riemannian manifold $M$. We prove that if $\Sigma$ is locally a regular intrinsic graph, the characteristic curves are of class $C^2$. The result is shape and improves the ones contained in \cite{MR2583494} and \cite{GalRit15}.