Curvature estimates for minimal hypersurfaces in the Heisenberg group

Abstract

This paper examines minimal hypersurfaces in sub-Riemannian Heisenberg groups. We extend the celebrated Simons formula and Kato inequality to the sub-Riemannian setting, and we apply them to obtain integral curvature estimates for stable hypersurfaces. These results lead to structural conditions that imply a Bernstein-type rigidity theorem for smooth, non-characteristic hypersurfaces in the second Heisenberg group.

With respect to the previous version, we removed one assumption from the proof of the Simons formula and we added several instances to justify some structural properties we introduced