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

Article

Abstract

In this paper we consider surfaces of class \(C^1\) with continuous prescribed mean curvature in three-dimensional contact sub-Riemannian manifolds and prove that their characteristic curves are of class \(C^2\). This regularity also holds for critical points of the sub-Riemannian perimeter under a volume constraint. All results are valid in the first Heisenberg group \({\mathbb {H}}^1\).

Mathematics Subject Classification

53C17 49Q20 

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di BolognaBolognaItaly
  2. 2.Departamento de Geometría y TopologíaUniversidad de GranadaGranadaSpain

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