Differential Harnack inequalities on Riemannian manifolds I : linear heat equation
| dc.creator | Li, Junfang | |
| dc.creator | Xu, Xiangjin | |
| dc.date | 2009-01-24 | |
| dc.date.accessioned | 2026-07-07T12:34:24Z | |
| dc.date.available | 2026-07-07T12:34:24Z | |
| dc.description | 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 $Ricci(M)\ge -k$, $k\in \mathbb R$. 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. | |
| dc.identifier | https://arxiv.org/abs/0901.3849 | |
| dc.identifier | http://arxiv.org/abs/0901.3849 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/217419 | |
| dc.subject | Differential Geometry | |
| dc.subject | 58G11 | |
| dc.title | Differential Harnack inequalities on Riemannian manifolds I : linear heat equation | |
| dc.type | text |