An Upper Bound for Hessian Matrices of Positive Solutions of Heat   Equations
  We prove global and local upper bounds for the Hessian of log positive solutions of the heat equation on a Riemannian manifold. The metric is either fixed or evolves under the Ricci flow. These upper bounds supplement the well-known global lower bound. 
Qing Han and Qi S Zhang
math.AP math.DG