Homological $n$-systole in $(n+1)$-manifolds and bi-Ricci curvature
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913565720444928 |
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| author | Chu, Jianchun Lee, Man-Chun Zhu, Jintian |
| author_facet | Chu, Jianchun Lee, Man-Chun Zhu, Jintian |
| contents | In this paper, we prove an optimal systolic inequality and the corresponding rigidity in the equality case on closed manifolds with positive bi-Ricci curvature, which generalizes the work of Bray-Brendle-Neves. The proof is given in all dimensions based on the method of minimal surfaces under the Generic Regularity Hypothesis, which is known to be true up to dimension ten. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20785 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homological $n$-systole in $(n+1)$-manifolds and bi-Ricci curvature Chu, Jianchun Lee, Man-Chun Zhu, Jintian Differential Geometry In this paper, we prove an optimal systolic inequality and the corresponding rigidity in the equality case on closed manifolds with positive bi-Ricci curvature, which generalizes the work of Bray-Brendle-Neves. The proof is given in all dimensions based on the method of minimal surfaces under the Generic Regularity Hypothesis, which is known to be true up to dimension ten. |
| title | Homological $n$-systole in $(n+1)$-manifolds and bi-Ricci curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2410.20785 |