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

Capogna, Luca; Citti, Giovanna; Manfredini, Maria

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

Authors

Capogna, Luca

Citti, Giovanna

Manfredini, Maria

Description

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.