Indiana University Mathematics Journal
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 apriori estimates on the solutions of the approximating Riemannian PDE and the ensuing C∞ regularity of the sub-Riemannian minimal surface along its Legendrian foliation.
Minimal surfaces, Sub-Riemannian geometry, Viscosity solutions
Capogna, Luca; Citti, Giovanna; and Manfredini, Maria, "Regularity of Non-Characteristic Minimal Graphs in the Heisenberg Group ℍ1" (2009). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.