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math.DG2025
Shi-type and Hamilton-type gradient estimates for a general parabolic equation under compact Finsler geometric flows
Yijie Miao, Bin Shen
Recently, the Li-Yau-type gradient estimates for positive solutions to parabolic equations \begin{equation} \partial_t u=Îu+\mathcal{R}_1u+\mathcal{R}_2u^α+\mathcal{R}_3u(\log u)…
math.DG2025
Feasibility of Nash-Moser iteration for Cheng-Yau-type gradient estimates of nonlinear equations on complete Riemannian manifolds
Bin Shen, Yuhan Zhu
In this manuscript, we employ the Nash-Moser iteration technique to determine a condition under which the positive solution of the generalized nonlinear Poisson equation $$\ope…