Abstract This paper derives elliptic gradient estimates for positive solutions to a nonlinear parabolic equation defined on a complete weighted Riemannian manifold. Applications of these estimates yield Liouville-type theorem, parabolic Harnack inequalities and bounds on weighted heat kernel on the lower boundedness assumption for Bakry-Émery curvature tensor.

中文翻译：

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加权非线性抛物线方程的梯度估计及其应用

摘要 本文推导了定义在完整加权黎曼流形上的非线性抛物线方程正解的椭圆梯度估计。这些估计的应用产生 Liouville 型定理、抛物线 Harnack 不等式和 Bakry-Émery 曲率张量下界假设下加权热核的边界。