Remarks on Li-Yau inequality on graphs
classification
🧮 math.DG
math.CO
keywords
estimatesgraphsgradientheatli-yauapplicationsbauerbhllmy
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In this paper, we study Li-Yau gradient estimates for the solutions $u$ to the heat equation $\partial_tu=\Delta u$ 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.
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