A Steklov eigenvalue estimate for affine connections and its application to substatic triples
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913787642118144 |
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| author | Fujitani, Yasuaki |
| author_facet | Fujitani, Yasuaki |
| contents | Choi-Wang obtained a lower bound of the first eigenvalue of the Laplacian on closed minimal hypersurfaces. On minimal hypersurfaces with boundary, Fraser-Li established an inequality giving a lower bound of the first Steklov eigenvalue as a counterpart of the Choi-Wang type inequality. These inequalities were shown under lower bounds of the Ricci curvature. In this paper, under non-negative Ricci curvature associated with an affine connection introduced by Wylie-Yeroshkin, we give a generalization of Fraser-Li type inequality. Our results hold not only for weighted manifolds under non-negative $1$-weighted Ricci curvature but also for substatic triples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07889 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Steklov eigenvalue estimate for affine connections and its application to substatic triples Fujitani, Yasuaki Differential Geometry Choi-Wang obtained a lower bound of the first eigenvalue of the Laplacian on closed minimal hypersurfaces. On minimal hypersurfaces with boundary, Fraser-Li established an inequality giving a lower bound of the first Steklov eigenvalue as a counterpart of the Choi-Wang type inequality. These inequalities were shown under lower bounds of the Ricci curvature. In this paper, under non-negative Ricci curvature associated with an affine connection introduced by Wylie-Yeroshkin, we give a generalization of Fraser-Li type inequality. Our results hold not only for weighted manifolds under non-negative $1$-weighted Ricci curvature but also for substatic triples. |
| title | A Steklov eigenvalue estimate for affine connections and its application to substatic triples |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2504.07889 |