Calculus of Variations and Geometric Measure Theory

N. Garofalo - A. Mondino

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

created by mondino on 03 Jun 2013
modified on 19 Oct 2013


Accepted Paper

Inserted: 3 jun 2013
Last Updated: 19 oct 2013

Journal: Nonlinear Analysis TMA
Year: 2013


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.

Tags: GeMeThNES