Local Li-Yau's estimates on $RCD^*(K,N)$ metric measure spaces

Published 17 Feb 2016 in math.DG and math.MG | (1602.05347v3)

Abstract: In this paper, we will study the (linear) geometric analysis on metric measure spaces. We will establish a local Li-Yau's estimate for weak solutions of the heat equation and prove a sharp Yau's gradient gradient for harmonic functions on metric measure spaces, under the Riemannian curvature-dimension condition $RCD^*(K,N).$

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