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.
Regularity of non-characteristic minimal graphs in the Heisenberg group $mathbb{H}^{1}$ / L. Capogna; G. Citti; M. Manfredini. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - STAMPA. - 58:(2009), pp. 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.
