Laplace comparison on Kähler Ricci flow and convergence
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911238710099968 |
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| author | Tian, Gang Zhang, Qi S. Zhang, Zhenlei Zhu, Meng Zhu, Xiaohua |
| author_facet | Tian, Gang Zhang, Qi S. Zhang, Zhenlei Zhu, Meng Zhu, Xiaohua |
| contents | We first prove a uniform integral Laplace comparison result for the Kähler Ricci flow on Fano manifolds which depends only on the initial metric. As an application, using Cheeger-Colding theory and previous results by some of the authors, we give a direct and independent proof of the Hamilton-Tian conjecture on convergence of Kähler-Ricci flows, modulo a codimension 4 singular set. We also expounded on some existing literature on this conjecture. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_14820 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Laplace comparison on Kähler Ricci flow and convergence Tian, Gang Zhang, Qi S. Zhang, Zhenlei Zhu, Meng Zhu, Xiaohua Differential Geometry 53E20, 53E30, 53C23 We first prove a uniform integral Laplace comparison result for the Kähler Ricci flow on Fano manifolds which depends only on the initial metric. As an application, using Cheeger-Colding theory and previous results by some of the authors, we give a direct and independent proof of the Hamilton-Tian conjecture on convergence of Kähler-Ricci flows, modulo a codimension 4 singular set. We also expounded on some existing literature on this conjecture. |
| title | Laplace comparison on Kähler Ricci flow and convergence |
| topic | Differential Geometry 53E20, 53E30, 53C23 |
| url | https://arxiv.org/abs/2509.14820 |