An improvement of regularity result for pseudo Calabi flow
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866912975214870528 |
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| author | Cheng, Jingrui Tian, Junhao |
| author_facet | Cheng, Jingrui Tian, Junhao |
| contents | In this paper, we observe that if the initial data of pseudo Calabi flow has volume form $C^0$ close to a smooth one, then the flow is immediately smooth for $t>0$. As an application, we show that if the initial data has volume form $C^0$ close to that of a cscK metric, then the pseudo Calabi flow exists for $t\in (0,+\infty)$. We also prove similar improvement of regularity and long time existence result for pseudo Calabi flow on a Fano manifold when the volume form is bounded and the class is close to $c_1(M)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19405 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An improvement of regularity result for pseudo Calabi flow Cheng, Jingrui Tian, Junhao Differential Geometry Analysis of PDEs In this paper, we observe that if the initial data of pseudo Calabi flow has volume form $C^0$ close to a smooth one, then the flow is immediately smooth for $t>0$. As an application, we show that if the initial data has volume form $C^0$ close to that of a cscK metric, then the pseudo Calabi flow exists for $t\in (0,+\infty)$. We also prove similar improvement of regularity and long time existence result for pseudo Calabi flow on a Fano manifold when the volume form is bounded and the class is close to $c_1(M)$. |
| title | An improvement of regularity result for pseudo Calabi flow |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2603.19405 |