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- W2950348399 abstract "In the first part of this paper, we get new Li-Yau type gradient estimates for positive solutions of heat equation on Riemmannian manifolds with $Ricci(M)ge -k$, $kin mathbb R$. As applications, several parabolic Harnack inequalities are obtained and they lead to new estimates on heat kernels of manifolds with Ricci curvature bounded from below. In the second part, we establish a Perelman type Li-Yau-Hamilton differential Harnack inequality for heat kernels on manifolds with $Ricci(M)ge -k$, which generalizes a result of L. Ni cite{NL1,NL4}. As applications, we obtain new Harnack inequalities and heat kernel estimates on general manifolds. We also obtain various entropy monotonicity formulas for all compact Riemannian manifolds." @default.
- W2950348399 created "2019-06-27" @default.
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- W2950348399 date "2009-01-24" @default.
- W2950348399 modified "2023-09-27" @default.
- W2950348399 title "Differential Harnack inequalities on Riemannian manifolds I : linear heat equation" @default.
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