Stability of weighted minimal hypersurfaces under a lower $1$-weighted Ricci curvature bound
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912892549332992 |
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| author | Fujitani, Yasuaki Sakurai, Yohei |
| author_facet | Fujitani, Yasuaki Sakurai, Yohei |
| contents | We will study the $1$-weighted Ricci curvature in view of the extrinsic geometric analysis. We derive several geometric consequences concerning stable weighted minimal hypersurfaces in weighted manifolds under a lower $1$-weighted Ricci curvature bound. We prove a Schoen-Yau type criterion, and conclude a structure theorem for three-dimensional weighted manifolds of non-negative $1$-weighted Ricci curvature. We also show non-existence results under volume growth conditions, and conclude smooth compactness theorems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20405 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of weighted minimal hypersurfaces under a lower $1$-weighted Ricci curvature bound Fujitani, Yasuaki Sakurai, Yohei Differential Geometry We will study the $1$-weighted Ricci curvature in view of the extrinsic geometric analysis. We derive several geometric consequences concerning stable weighted minimal hypersurfaces in weighted manifolds under a lower $1$-weighted Ricci curvature bound. We prove a Schoen-Yau type criterion, and conclude a structure theorem for three-dimensional weighted manifolds of non-negative $1$-weighted Ricci curvature. We also show non-existence results under volume growth conditions, and conclude smooth compactness theorems. |
| title | Stability of weighted minimal hypersurfaces under a lower $1$-weighted Ricci curvature bound |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2508.20405 |