Parabolic frequency monotonicity for two nonlinear equations under Ricci flow
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910921030369280 |
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| author | Li, Chuanhuan Li, Yi Xu, Kairui Zhu, Jichun |
| author_facet | Li, Chuanhuan Li, Yi Xu, Kairui Zhu, Jichun |
| contents | In this paper, we consider the parabolic frequency for positive solutions of two nonlinear parabolic equations under the Ricci flow on closed manifolds. We obtain the monotonicity of parabolic frequency for the solution of two nonlinear parabolic equations with bounded Ricci curvature, then we apply the parabolic frequency monotonicity to get some integral type Harnack inequalities and we use -K1 instead of the lower bound 0 of Ricci curvature from Theorem 4.3 in 16, where K1 is any positive constant. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_14912 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Parabolic frequency monotonicity for two nonlinear equations under Ricci flow Li, Chuanhuan Li, Yi Xu, Kairui Zhu, Jichun Differential Geometry Analysis of PDEs In this paper, we consider the parabolic frequency for positive solutions of two nonlinear parabolic equations under the Ricci flow on closed manifolds. We obtain the monotonicity of parabolic frequency for the solution of two nonlinear parabolic equations with bounded Ricci curvature, then we apply the parabolic frequency monotonicity to get some integral type Harnack inequalities and we use -K1 instead of the lower bound 0 of Ricci curvature from Theorem 4.3 in 16, where K1 is any positive constant. |
| title | Parabolic frequency monotonicity for two nonlinear equations under Ricci flow |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2310.14912 |