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Regularity of non-characteristic minimal graphs in the Heisenberg group \(\mathbb{H}^{1}\). (English) Zbl 1182.35087

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.

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
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