Remarks on Li-Yau inequality on graphs

Abstract

In this paper, we study Li-Yau gradient estimates for the solutions $u$ to the heat equation ${\partial }_{t}u=\Delta u$ on graphs under the curvature condition $CD(n,-K)$ introduced by Bauer et al. in \cite{BHLLMY}. As applications, we derive Harnack inequalities and heat kernel estimates on graphs. Also we present a type of Hamilton gradient estimates.

19 pages. arXiv admin note: text overlap with arXiv:1306.2561 by other authors

References in corpus (2)

• Subelliptic Li-Yau estimates on three dimensional model spaces
• Differential Harnack inequalities and Perelman type entropy formulae for subelliptic operators