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 (6)

• Minimal surfaces in the Heisenberg group
• The Bernstein Problem in the Heisenberg Group
• Area-stationary surfaces in the Heisenberg group H^1
• A notable family of entire intrinsic minimal graphs in the Heisenberg group which are not perimeter minimizing
• Instability of graphical strips and a positive answer to 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 (3)

• Regularity of minimal intrinsic graphs in 3 dimensional sub-Riemannian structures of step 2
• Uniform Gaussian bounds for subelliptic heat kernels and an application to the total variation flow of graphs over Carnot groups
• Regularity of C^{1} smooth surfaces with prescribed p-mean curvature in the Heisenberg group