Regularity of non-characteristic minimal graphs in the Heisenberg group $H^1$

Abstract

Minimal surfaces in the sub-Riemannian Heisenberg group can be constructed by means of a Riemannian approximation scheme, as limit of Riemannian minimal surfaces. We study the regularity of Lipschitz, non-characteristic minimal surfaces which arise as such limits. Our main results are a-priori estimates on the solutions of the approximating Riemannian PDE and the ensuing $C^{\infty }$ regularity of the sub-Riemannian minimal surface along its Legendrian foliation.

References in corpus (2)

• The Bernstein Problem in the Heisenberg Group
• Regularity of C^{1} smooth surfaces with prescribed p-mean curvature in the Heisenberg group

Cited by in corpus (1)

• Regularity of C^{1} smooth surfaces with prescribed p-mean curvature in the Heisenberg group