Expanding Soliton Models for Kähler-Ricci Flow Near Conical Singularities
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918527414304768 |
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| author | Chen, Longteng Hallgren, Max Lavoyer, Lucas |
| author_facet | Chen, Longteng Hallgren, Max Lavoyer, Lucas |
| contents | Let $(Y,g_0)$ be a compact analytic space with a finite number of singular points, where the metric at each singular point is modelled on a Kähler cone with smooth canonical model. We show that the Kähler-Ricci flow with such initial data satisfies a $C/t$ curvature bound, and that the flow near each singular point is modelled on the unique Kähler-Ricci expander asymptotic to the corresponding cone. Our motivation is to give a geometric description of the Kähler--Ricci flow emerging from singularities arising in the analytic minimal model program. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04223 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Expanding Soliton Models for Kähler-Ricci Flow Near Conical Singularities Chen, Longteng Hallgren, Max Lavoyer, Lucas Differential Geometry Analysis of PDEs Let $(Y,g_0)$ be a compact analytic space with a finite number of singular points, where the metric at each singular point is modelled on a Kähler cone with smooth canonical model. We show that the Kähler-Ricci flow with such initial data satisfies a $C/t$ curvature bound, and that the flow near each singular point is modelled on the unique Kähler-Ricci expander asymptotic to the corresponding cone. Our motivation is to give a geometric description of the Kähler--Ricci flow emerging from singularities arising in the analytic minimal model program. |
| title | Expanding Soliton Models for Kähler-Ricci Flow Near Conical Singularities |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2604.04223 |