  In this paper we derive Cheng-Yau, Li-Yau, Hamilton estimates for Riemannian
manifolds with Bakry-Emery Ricci curvature bounded from below, and also global
and local upper bounds, in terms of Bakry-Emery Ricci curvature, for the
Hessian of positive and bounded solutions of the weighted heat equation on a
closed Riemannian manifold.
