Comparison Theorems and the Intermediate Ricci Curvature Assumption
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908589320306688 |
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| author | Wu, Yujie |
| author_facet | Wu, Yujie |
| contents | We explore the notion of m-intermediate Ricci curvature assumption introduced by Brendle-Hirsch-Johne further. If a manifold has non-negative m-intermediate Ricci curvature and stable weighted slicing of order m-1, then the last slice has almost non-negative Ricci curvature in the spectral sense. We prove comparison theorems on the diameter and in-radius bound for stable weighted (respectively free boundary) slicing in such manifolds (respectively with mean convex boundary). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11205 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Comparison Theorems and the Intermediate Ricci Curvature Assumption Wu, Yujie Differential Geometry We explore the notion of m-intermediate Ricci curvature assumption introduced by Brendle-Hirsch-Johne further. If a manifold has non-negative m-intermediate Ricci curvature and stable weighted slicing of order m-1, then the last slice has almost non-negative Ricci curvature in the spectral sense. We prove comparison theorems on the diameter and in-radius bound for stable weighted (respectively free boundary) slicing in such manifolds (respectively with mean convex boundary). |
| title | Comparison Theorems and the Intermediate Ricci Curvature Assumption |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2510.11205 |