Regularity of non-characteristic minimal graphs in the Heisenberg group $H^1$
By Luca Capogna, Giovanna Citti, Maria Manfredini. 2008
57 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/ff1d5950f8c4545a7e6aa4fdb11300a831a8e8e0
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In Applied Mathematics
- Jih-Hsin Cheng
- Jenn-Fang Hwang
- Paul Yang
- Scott D. Pauls
- Manuel Ritor'e
- Giovanna Citti
- Maria Manfredini
- Luca Capogna
In Geometry and Topology
- Jih-Hsin Cheng
- Jenn-Fang Hwang
- Paul Yang
- Scott D. Pauls
- Manuel Ritor'e
- A. Malchiodi
- Yanyan Li
- Francesco Serra Cassano
Citations in the corpus
- Regularity of C1 smooth surfaces with prescribed p-mean curvature in the Heisenberg group (2007, result): “the idea of conveying information along the characteristic curves from the study of hyperbolic P.D.E. ([12]). After this paper was submitted, we were informed of recent results about regularity ([2], [3]) by the referee. In [3], Capogna, Citti, and Manfredini proved an interesting result, among othe”