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arXiv · 2409.20359

Curvature estimates for minimal hypersurfaces in the Heisenberg group

Gianmarco Giovannardi·Andrea Pinamonti·Simone Verzellesi
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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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Gianmarco Giovannardi, Andrea Pinamonti, Simone Verzellesi. 2024-09-30. Curvature estimates for minimal hypersurfaces in the Heisenberg group. https://arxiv.org/abs/2409.20359

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