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

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

2008-04-21

arxiv.org/abs/0804.3406v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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