IUMJ

Title: Regularity of non-characteristic minimal graphs in the Heisenberg group $\mathbb{H}^{1}$

Authors: Luca Capogna, Giovanna Citti and Maria Manfredini

Issue: Volume 58 (2009), Issue 5, 2115-2160

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 approxi mating Riemannian PDE and the ensuing $C^{\infty}$ regularity of the sub-Riemannian minimal surface along its Legendrian foliation.