Regularity of C¹ surfaces with prescribed mean curvature in three-dimensional contact sub-Riemannian manifolds

2015/01/28 by Matteo Galli, Galli, Matteo, Manuel Ritoré +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.DG

paper · pdf · doi:10.48550/arxiv.1501.07246

12 pages. Final version to appear in Calc. Var. PDE

openalex publication_date 2015/01/28 · arxiv created 2015/05/01 · arxiv updated 2015/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider surfaces of class C¹ with continuous prescribed mean curvature in a three-dimensional contact sub-Riemannian manifold and prove that their characteristic curves are of class C². 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 ℍ¹.

Citations

• Riemannian Geometry of Contact and Symplectic Manifolds
• Area-stationary and stable surfaces of class C¹ in the sub-Riemannian\n Heisenberg group mathbb H¹

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• The regularity of Euclidean Lipschitz boundaries with prescribed mean curvature in three-dimensional contact sub-Riemannian manifolds
• Complete stable CMC surfaces with empty singular set in Sasakian sub-Riemannian 3-manifolds
• Minimal surfaces in contact Sub-Riemannian manifolds
• Curvature measures and the sub-Riemannian Gauss-Bonnet theorem