Space of Ricci flows (II)—Part B: Weak compactness of the flows

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 Kahler Ricci flows with proper geometric bounds. Our theory is a generalization of the structure theory of non-collapsed Kahler Einstein manifolds. As applications, we show the convergence of the Kahler Ricci flow in an appropriate topology and prove the partial-$C^0$-conjecture.