Characterization of Einstein-Fano manifolds via the K\"ahler-Ricci flow

Abstract

We explain a characterization of Einstein-Fano manifolds in terms of the lower bound of the density of the volume of the K\"ahler-Ricci Flow. This is a direct consequence of Perelman's uniform estimate for the K\"ahler-Ricci Flow and a C0 estimate of Tian and Zhu.

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