Space of Ricci flows (II)

Abstract

Based on the compactness of the moduli of non-collapsed Calabi-Yau spaces with mild singularities, we set up a structure theory for polarized K\"ahler Ricci flows with proper geometric bounds. Our theory is a generalization of the structure theory of non-collapsed K\"ahler Einstein manifolds. As applications, we prove the Hamilton-Tian conjecture and the partial-$C^0$-conjecture of Tian.