Gradient estimation of a generalized non-linear heat type equation along Super-Perelman Ricci flow on weighted Riemannian manifolds
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912190051647488 |
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| author | Li, Yanlin Abolarinwa, Abimbola Ghosh, Suraj Hui, Shyamal Kumar |
| author_facet | Li, Yanlin Abolarinwa, Abimbola Ghosh, Suraj Hui, Shyamal Kumar |
| contents | In this article we derive gradient estimation for positive solution of the equation \begin{equation*} (\partial_t-Δ_f)u = A(u)p(x,t) + B(u)q(x,t) + \mathcal{G}(u) \end{equation*} on a weighted Riemannian manifold evolving along the $(k,m)$ super Perelman-Ricci flow \begin{equation*} \frac{\partial g}{\partial t}(x,t)+2Ric_f^m(g)(x,t)\ge -2kg(x,t). \end{equation*} As an application of gradient estimation we derive a Harnack type inequality along with a Liouville type theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15705 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gradient estimation of a generalized non-linear heat type equation along Super-Perelman Ricci flow on weighted Riemannian manifolds Li, Yanlin Abolarinwa, Abimbola Ghosh, Suraj Hui, Shyamal Kumar Differential Geometry Analysis of PDEs 53C21, 58J60, 58J35 In this article we derive gradient estimation for positive solution of the equation \begin{equation*} (\partial_t-Δ_f)u = A(u)p(x,t) + B(u)q(x,t) + \mathcal{G}(u) \end{equation*} on a weighted Riemannian manifold evolving along the $(k,m)$ super Perelman-Ricci flow \begin{equation*} \frac{\partial g}{\partial t}(x,t)+2Ric_f^m(g)(x,t)\ge -2kg(x,t). \end{equation*} As an application of gradient estimation we derive a Harnack type inequality along with a Liouville type theorem. |
| title | Gradient estimation of a generalized non-linear heat type equation along Super-Perelman Ricci flow on weighted Riemannian manifolds |
| topic | Differential Geometry Analysis of PDEs 53C21, 58J60, 58J35 |
| url | https://arxiv.org/abs/2404.15705 |