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THE KÄHLER-RICCI FLOW AND K-POLYSTABILITY
American Journal of Mathematics
Vol. 132, No. 4 (August 2010), pp. 1077-1090
Published by: The Johns Hopkins University Press
Stable URL: http://www.jstor.org/stable/40864469
Page Count: 14
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We consider the Kähler-Ricci flow on a Fano manifold. We show that if the curvature remains uniformly bounded along the flow, the Mabuchi energy is bounded below, and the manifold is K-polystable, then the manifold admits a Kähler-Einstein metric. The main ingredient is a result that says that a sufficiently small perturbation of a cscK manifold admits a cscK metric if it is K-polystable.
American Journal of Mathematics © 2010 The Johns Hopkins University Press