Bergman Kernel Along The Kähler Ricci Flow and Tian's Conjecture

In this paper, we study the behavior of Bergman kernels along the Kähler Ricci flow on Fano manifolds. We show that the Bergman kernels are equivalent along the Kähler Ricci flow under certain condition on the Ricci curvature of the initial metric. Then, using a recent work of Tian and Zhang, we can solve a conjecture of Tian for Fano manifolds of complex dimension $\le 3$.

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