Strong uniqueness of tangent flows at cylindrical singularities in Ricci flow
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917393527209984 |
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| author | Fang, Hanbing Li, Yu |
| author_facet | Fang, Hanbing Li, Yu |
| contents | In this paper, we establish a Lojasiewicz inequality for the pointed $\mathcal{W}$-entropy in the Ricci flow, under the assumption that the geometry near the base point is close to a standard cylinder $\mathbb{R}^k \times S^{n-k}$ or the quotient thereof. As an application, we prove the strong uniqueness of the cylindrical tangent flow at the first singular time of the Ricci flow. Specifically, we show that the modified Ricci flow near the singularity converges to the cylindrical model under a fixed gauge. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20320 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong uniqueness of tangent flows at cylindrical singularities in Ricci flow Fang, Hanbing Li, Yu Differential Geometry In this paper, we establish a Lojasiewicz inequality for the pointed $\mathcal{W}$-entropy in the Ricci flow, under the assumption that the geometry near the base point is close to a standard cylinder $\mathbb{R}^k \times S^{n-k}$ or the quotient thereof. As an application, we prove the strong uniqueness of the cylindrical tangent flow at the first singular time of the Ricci flow. Specifically, we show that the modified Ricci flow near the singularity converges to the cylindrical model under a fixed gauge. |
| title | Strong uniqueness of tangent flows at cylindrical singularities in Ricci flow |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2510.20320 |