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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.15744 |
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| _version_ | 1866914071961403392 |
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| author | Fujitani, Yasuaki Sakurai, Yohei |
| author_facet | Fujitani, Yasuaki Sakurai, Yohei |
| contents | We develop geometric analysis on weighted Riemannian manifolds under lower $0$-weighted Ricci curvature bounds. Under such curvature bounds, we prove a first non-zero Steklov eigenvalue estimate of Wang-Xia type on compact weighted manifolds with boundary, and a first non-zero eigenvalue estimate of Choi-Wang type on closed weighted minimal hypersurfaces. We also produce an ABP estimate and a Sobolev inequality of Brendle type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15744 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric analysis on weighted manifolds under lower $0$-weighted Ricci curvature bounds Fujitani, Yasuaki Sakurai, Yohei Differential Geometry We develop geometric analysis on weighted Riemannian manifolds under lower $0$-weighted Ricci curvature bounds. Under such curvature bounds, we prove a first non-zero Steklov eigenvalue estimate of Wang-Xia type on compact weighted manifolds with boundary, and a first non-zero eigenvalue estimate of Choi-Wang type on closed weighted minimal hypersurfaces. We also produce an ABP estimate and a Sobolev inequality of Brendle type. |
| title | Geometric analysis on weighted manifolds under lower $0$-weighted Ricci curvature bounds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2408.15744 |