Abstract In this paper, we prove matrix and classical Harnack estimates for positive solutions to the nonlinear diffusion partial differential equation ∂ t u = Δ u + a u + b u p + 1 on a compact Kahler manifold (with fixed metric). When the metric evolves under the normalized Kahler–Ricci flow, we also derive some matrix and classical Harnack estimates.

中文翻译：

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紧致 Kähler 流形上非线性扩散方程的 Harnack 估计

摘要 在本文中，我们证明了非线性扩散偏微分方程 ∂ tu = Δ u + au + bup + 1 在紧凑 Kahler 流形（具有固定度量）上的正解的矩阵和经典 Harnack 估计。当度量在归一化 Kahler-Ricci 流下演化时，我们还会推导出一些矩阵和经典 Harnack 估计。