Tian's partial $C^0$-estimate implies Hamilton-Tian's conjecture

Abstract

In this paper, we prove the Hamilton-Tian conjecture for Kähler-Ricci flow based on a recent work of Liu-Székelyhidi on Tian's partical $C^0$-estimate for poralized Kähler metrics with Ricci bounded below. The Yau-Tian-Donaldson conjecture for the existence of Kähler-Einstein metrics on Fano manifolds will be also discussed.

We added Lemma 4.4 and modified the proofs of Proposition 4.7 and Lemma 4.8