On the structure of noncollapsed Ricci flow limit spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915925383446528 |
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| author | Fang, Hanbing Li, Yu |
| author_facet | Fang, Hanbing Li, Yu |
| contents | We establish a weak compactness theorem for the moduli space of closed Ricci flows with uniformly bounded entropy, each equipped with a natural spacetime distance, under pointed Gromov-Hausdorff convergence. Furthermore, we develop a structure theory for the corresponding Ricci flow limit spaces, showing that the regular part, where convergence is smooth, admits the structure of a Ricci flow spacetime, while the singular set has codimension at least four. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12398 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the structure of noncollapsed Ricci flow limit spaces Fang, Hanbing Li, Yu Differential Geometry We establish a weak compactness theorem for the moduli space of closed Ricci flows with uniformly bounded entropy, each equipped with a natural spacetime distance, under pointed Gromov-Hausdorff convergence. Furthermore, we develop a structure theory for the corresponding Ricci flow limit spaces, showing that the regular part, where convergence is smooth, admits the structure of a Ricci flow spacetime, while the singular set has codimension at least four. |
| title | On the structure of noncollapsed Ricci flow limit spaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2510.12398 |