Regularity of Kähler–Ricci flows on Fano manifolds

Abstract

In this paper, we will establish a regularity theory for the Kahler–Ricci flow on Fano n-manifolds with Ricci curvature bounded in L p -norm for some $${p > n}$$ . Using this regularity theory, we will also solve a long-standing conjecture for dimension 3. As an application, we give a new proof of the Yau–Tian–Donaldson conjecture for Fano 3-manifolds. The results have been announced in [45].