@inproceedings{Szkelyhidi2009TheKF,
title={The K{\"a}hler-Ricci flow and K-polystability},
author={G{\'a}bor Sz{\'e}kelyhidi},
year={2009}
}

Gábor Székelyhidi

Published 2009

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.