Characterization of Einstein-Fano manifolds via the K\"ahler-Ricci flow
Nefton Pali
32U05complex-Monge-Ampere equations
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 $\frac{1}{2}$.
Indiana University Mathematics Journal
2008
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10.1512/iumj.2008.57.3426
10.1512/iumj.2008.57.3426
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Indiana Univ. Math. J. 57 (2008) 3241 - 3274
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