Curvature estimates for minimal hypersurfaces in the Heisenberg group
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915309053542400 |
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| author | Giovannardi, Gianmarco Pinamonti, Andrea Verzellesi, Simone |
| author_facet | Giovannardi, Gianmarco Pinamonti, Andrea Verzellesi, Simone |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20359 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Curvature estimates for minimal hypersurfaces in the Heisenberg group Giovannardi, Gianmarco Pinamonti, Andrea Verzellesi, Simone Differential Geometry 53C17, 53A10, 35R03 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. |
| title | Curvature estimates for minimal hypersurfaces in the Heisenberg group |
| topic | Differential Geometry 53C17, 53A10, 35R03 |
| url | https://arxiv.org/abs/2409.20359 |