The structure and rigidiy of FBCMC hypersurfaces
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909815742136320 |
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| author | Li, Jia |
| author_facet | Li, Jia |
| contents | We prove that the combination of strict positivity of $k$-tri-Ricci curvature with non-negative $3$-intermediate Ricci curvature forces rigidity of two-sided stable free boundary minimal hypersurface in a 5-manifold with bounded geometry and weakly convex boundary. This improves the result of Wu \cite{Wuyujie2023} to 5-dimensions and also extends the method of Hong-Yan \cite{Hong-cmc nonexis} to the free boundary case. We give a characterization of one-endedness for weakly stable free boundary constant mean curvature(FBCMC) hypersurfaces, which is an extension of Cheng-Cheung-Zhou \cite{Cheng-Cheung-Zhou2008}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11739 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The structure and rigidiy of FBCMC hypersurfaces Li, Jia Differential Geometry We prove that the combination of strict positivity of $k$-tri-Ricci curvature with non-negative $3$-intermediate Ricci curvature forces rigidity of two-sided stable free boundary minimal hypersurface in a 5-manifold with bounded geometry and weakly convex boundary. This improves the result of Wu \cite{Wuyujie2023} to 5-dimensions and also extends the method of Hong-Yan \cite{Hong-cmc nonexis} to the free boundary case. We give a characterization of one-endedness for weakly stable free boundary constant mean curvature(FBCMC) hypersurfaces, which is an extension of Cheng-Cheung-Zhou \cite{Cheng-Cheung-Zhou2008}. |
| title | The structure and rigidiy of FBCMC hypersurfaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2502.11739 |