  In this paper, we systematically study the heat kernel of the Ricci flows
induced by Ricci shrinkers. We develop several estimates which are much sharper
than their counterparts in general closed Ricci flows. Many classical results,
including the optimal Logarithmic Sobolev constant estimate, the Sobolev
constant estimate, the no-local-collapsing theorem, the pseudo-locality theorem
and the strong maximum principle for curvature tensors, are essentially
improved for Ricci flows induced by Ricci shrinkers. Our results provide many
necessary tools to analyze short time singularities of the Ricci flows of
general dimension.
