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The Kähler-Ricci flow and K-polystability
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 132, Number 4, August 2010
- pp. 1077-1090
- 10.1353/ajm.0.0128
- Article
- Additional Information
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We consider the K\"ahler-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 K\"ahler-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.