Curvature estimates for minimal hypersurfaces in the Heisenberg group
Differential Geometry
2025-05-29 v2
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.
Cite
@article{arxiv.2409.20359,
title = {Curvature estimates for minimal hypersurfaces in the Heisenberg group},
author = {Gianmarco Giovannardi and Andrea Pinamonti and Simone Verzellesi},
journal= {arXiv preprint arXiv:2409.20359},
year = {2025}
}
Comments
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