English

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.

Keywords

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

R2 v1 2026-06-21T10:20:34.278Z