IUMJ

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

Authors: Nefton Pali

Issue: Volume 57 (2008), Issue 7, 3241-3274

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 consequence of Perelman's uniform estimate for the K\"ahler-Ricci Flow and a $C^0$ estimate of Tian and Zhu. We remark also a new monotonicity of Perelman's $\mathscr{W}$ functional along the K\"ahler-Ricci Flow with respect to the Ricci potential with scale factor $\frac{1}{2}$.