Hamilton's Gradient Estimates and A Monotonicity Formula for Heat Flows on Metric Measure Spaces

Abstract

In this paper, we extend the Hamilton's gradient estimates \cite{har93} and a monotonicity formula of entropy \cite{ni04} for heat flows from smooth Riemannian manifolds to (non-smooth) metric measure spaces with appropriate Riemannian curvature-dimension condition.

arXiv comment19 pages, In a special issue of Nonlinear Analysis (vol 131,2016,32-47): Qualitative and Quantitative Properties of Solutions to Parabolic Equations,in Honor of Victor A. Galaktionov for his 60th Birthday, Edited By Thierry Coulhon, Neil Trudinger and Vincenzo Vespri

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Cited by in corpus (1)

• Sharp Heat Kernel Bounds and Entropy in Metric Measure Spaces