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arXiv · 1306.0494

Li-Yau and Harnack type inequalities in $RCD^*(K,N)$ metric measure spaces

Nicola Garofalo·Andrea Mondino
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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.

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Nicola Garofalo, Andrea Mondino. 2013-06-03. Li-Yau and Harnack type inequalities in $RCD^*(K,N)$ metric measure spaces. https://doi.org/10.1016/j.na.2013.10.002

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