Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915328018087936 |
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| author | Lu, Juanling Zheng, Yu |
| author_facet | Lu, Juanling Zheng, Yu |
| contents | In this paper, we establish Li-Yau-type and Hamilton-type estimates for positive solutions to the heat equation associated with the generalized Ricci flow, under a less stringent curvature condition. Compared with [25] and [35], these estimates generalize the results in Ricci flow to this new flow under the weaker Ricci curvature bounded assumption. As an application, we derive the Harnack-type inequalities in spacetime and find the monotonicity of one parabolic frequency for positive solutions of the heat equation under bounded Ricci curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04937 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow Lu, Juanling Zheng, Yu Differential Geometry In this paper, we establish Li-Yau-type and Hamilton-type estimates for positive solutions to the heat equation associated with the generalized Ricci flow, under a less stringent curvature condition. Compared with [25] and [35], these estimates generalize the results in Ricci flow to this new flow under the weaker Ricci curvature bounded assumption. As an application, we derive the Harnack-type inequalities in spacetime and find the monotonicity of one parabolic frequency for positive solutions of the heat equation under bounded Ricci curvature. |
| title | Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2506.04937 |