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arXiv · 0803.1613

The Kahler-Ricci flow and K-stability

Gábor Székelyhidi
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Abstract

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.

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Gábor Székelyhidi. 2009-01-15. The Kahler-Ricci flow and K-stability. https://arxiv.org/abs/0803.1613

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