  In this paper we give Hamilton's Laplacian estimates for the heat equation on
complete noncompact manifolds with nonnegative Ricci curvature. As an
application, combining Li-Yau's lower and upper bounds of the heat kernel, we
give an estimate on Laplacian form of the heat kernel on complete manifolds
with nonnegative Ricci curvature that is sharp in the order of time parameter
for the heat kernel on the Euclidean space.
