Regularity of Kähler–Ricci flows on Fano manifolds

In this paper, we will establish a regularity theory for the Kähler–Ricci flow on Fano n-manifolds with Ricci curvature bounded in Lp-norm for some $${p > n}$$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].

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