The Kahler-Ricci flow and K-stability

Details The Kahler-Ricci flow and K-stability The Kahler-Ricci flow and K-stability

2008-03-11

arxiv.org/abs/0803.1613v2

Amer. J. Math. 132 (2010), 1077--1090

Mathematics

Differential Geometry

14 pages, corrected proof

Scientific paper

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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