Space of Ricci flows (II)

TL;DR

This paper develops a structure theory for polarized Kähler Ricci flows with bounds, generalizing previous theories for Calabi-Yau spaces, and proves significant conjectures in the field.

Contribution

It introduces a new structure theory for polarized Kähler Ricci flows based on moduli compactness, extending the understanding of non-collapsed Calabi-Yau spaces.

Findings

Proves the Hamilton-Tian conjecture.

Establishes the partial-$C^0$-conjecture of Tian.

Provides a framework for analyzing polarized Kähler Ricci 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 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.