Preprint

Inserted: 30 sep 2024
Last Updated: 29 may 2025

Year: 2024
Notes:

Compared to an earlier version, we removed one assumption from the proof of Simons' formula and added several examples to justify the structural properties we introduced

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.

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• Simons_Formula-6.pdf