Abstract

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.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1077-1090
Launched on MUSE
2010-07-31
Open Access
No
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