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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.14019 |
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| _version_ | 1866914096088088576 |
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| author | Gianniotis, Panagiotis |
| author_facet | Gianniotis, Panagiotis |
| contents | We prove that a three dimensional compact Ricci flow that encounters a Type I singularity has uniformly bounded diameter up to the singular time, thus giving an affirmative answer - for Type I singularities - to a conjecture of Perelman. To achieve this, we introduce a concept of a neck-region for a Ricci flow, analogous to the neck-regions introduced by Jiang-Naber and Cheeger-Jiang-Naber, in the study of Ricci limit spaces. We then prove that the associated packing measure is, in a certain sense, Ahlfors regular, a result that holds in any dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14019 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diameter bounds in 3d Type I Ricci flows Gianniotis, Panagiotis Differential Geometry Analysis of PDEs We prove that a three dimensional compact Ricci flow that encounters a Type I singularity has uniformly bounded diameter up to the singular time, thus giving an affirmative answer - for Type I singularities - to a conjecture of Perelman. To achieve this, we introduce a concept of a neck-region for a Ricci flow, analogous to the neck-regions introduced by Jiang-Naber and Cheeger-Jiang-Naber, in the study of Ricci limit spaces. We then prove that the associated packing measure is, in a certain sense, Ahlfors regular, a result that holds in any dimension. |
| title | Diameter bounds in 3d Type I Ricci flows |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2510.14019 |