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EnglishMinimal 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.
| Titolo: | Regularity of non-characteristic minimal graphs in the Heisenberg group $mathbb{H}^{1}$ |
| Autore/i: | L. Capogna; CITTI, GIOVANNA; MANFREDINI, MARIA |
| Autore/i Unibo: | |
| Anno: | 2009 |
| Rivista: | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1512/iumj.2009.58.3673 |
| 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. |
| Data prodotto definitivo in UGOV: | 2009-12-18 19:35:03 |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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http://hdl.handle.net/11585/81424
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