Capogna, Luca; Citti, Giovanna; Manfredini, Maria Regularity of non-characteristic minimal graphs in the Heisenberg group \(\mathbb{H}^{1}\). (English) Zbl 1182.35087 Indiana Univ. Math. J. 58, No. 5, 2115-2160 (2009). Minimal surfaces in the sub-Riemannian Heisenberg group can be constructed by means of a Riemannian approximation scheme, as limit of Riemannian minimal surfaces. The authors study the regularity of Lipschitz, non-characteristic minimal surfaces which arise as such limits. Their 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. Reviewer: Marco Biroli (Milano) Cited in 1 ReviewCited in 28 Documents MSC: 35H20 Subelliptic equations 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature 53A17 Differential geometric aspects in kinematics 35R03 PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. 35D40 Viscosity solutions to PDEs Keywords:sub-Riemannian geometry; minimal surfaces PDFBibTeX XMLCite \textit{L. Capogna} et al., Indiana Univ. Math. J. 58, No. 5, 2115--2160 (2009; Zbl 1182.35087) Full Text: DOI arXiv