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Li-Yau and Harnack type inequalities in $RCD^*(K,N)$ metric measure spaces (1306.0494v1)
Published 3 Jun 2013 in math.AP and math.MG
Abstract: Metric measure spaces satisfying the reduced curvature-dimension condition $CD*(K,N)$ and where the heat flow is linear are called $RCD*(K,N)$-spaces. This class of non smooth spaces contains Gromov-Hausdorff limits of Riemannian manifolds with Ricci curvature bounded below by $K$ and dimension bounded above by $N$. We prove that in $RCD*(K,N)$-spaces the following properties of the heat flow hold true: a Li-Yau type inequality, a Bakry-Qian inequality, the Harnack inequality.