Salvato in:
| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2402.00006 |
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Sommario:
- In this paper, we explore the positive solutions to the Finslerian nonlinear equation $$\frac{\partial u}{\partial t} = Δ^{\nabla u} u + au\log u + bu,$$ which is related to Ricci solitons and serves as the Euler-Lagrange equation to the Finslerian log-energy functional. We then obtain the global gradient estimate of its positive solution on a compact Finsler metric measure space with the weighted Ricci curvature bounded below. Furthermore, using a new comparison theorem developed by the first author, we also establish a local gradient estimate on a non-compact forward complete Finsler metric measure spaces with the mixed weighted Ricci curvature bounded below, as well as finite bounds of misalignment and some non-Riemannian curvatures. Lastly, we prove the Harnack inequalities and a Liouville-type theorem of such solutions.