The Kahler-Ricci flow and K-stability
Differential Geometry
2011-01-27 v2
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.
Cite
@article{arxiv.0803.1613,
title = {The Kahler-Ricci flow and K-stability},
author = {Gábor Székelyhidi},
journal= {arXiv preprint arXiv:0803.1613},
year = {2011}
}
Comments
14 pages, corrected proof