The Li-Yau Inequality and Heat Kernels on Metric Measure Spaces

2014/05/04 by Renjin Jiang, Jiang, Renjin · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #math.AP #math.DG #math.MG

paper · pdf · doi:10.48550/arxiv.1405.0684

31 pages, J. Math. Pures Appl., to appear

arxiv created 2014/10/30 · arxiv updated 2014/10/31

Abstract

Let (X,d,μ) be a RCD^∗(K, N) space with K∈ mathbbR and N∈ [1,∞). Suppose that (X,d) is connected, complete and separable, and \supp μ=X. We prove that the Li-Yau inequality for the heat flow holds true on (X,d,μ) when K≥ 0. A Baudoin-Garofalo inequality and Harnack inequalities for the heat flows are established on (X,d,μ) for general K∈ ℝ. Large time behaviors of heat kernels are also studied.

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