Hamilton's gradient estimates and a monotonicity formula for heat flows on metric measure spaces

In this paper, we extend the Hamilton's gradient estimates (Hamilton 1993) and a monotonicity formula of entropy (Ni 2004) for heat flows from smooth Riemannian manifolds to (non-smooth) metric measure spaces with appropriate Riemannian curvature-dimension condition. (C) 2015 Elsevier Ltd. All rights reserved.