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∞ regularity of the sub-Riemannian minimal surface along its Legendrian foliation.
L. Capogna, G. Citti, M. Manfredini (2009). Regularity of non-characteristic minimal graphs in the Heisenberg group $mathbb{H}^{1}$. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 58, 2115-2160 [10.1512/iumj.2009.58.3673].
Regularity of non-characteristic minimal graphs in the Heisenberg group $mathbb{H}^{1}$
CITTI, GIOVANNA;MANFREDINI, MARIA
2009
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∞ regularity of the sub-Riemannian minimal surface along its Legendrian foliation.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
