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 $mathbbH^1$ / Capogna, L.; Citti, G.; Manfredini, M.. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - 58:(2009), pp. 2115-2160. [10.1512/iumj.2009.58.3673]
Regularity of non-characteristic minimal graphs in the Heisenberg group $mathbbH^1$
M. Manfredini
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.
Pubblicazioni consigliate
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris
