The Kahler-Ricci flow and K-stability

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.

14 pages, corrected proof

References in corpus (5)

• Kahler geometry on toric manifolds, and some other manifolds with large symmetry
• The Kähler-Ricci flow with positive bisectional curvature
• K-stability of constant scalar curvature Kähler manifolds
• The Kähler-Ricci flow and the $\bar{\partial }$ operator on vector fields
• Constant scalar curvature metrics on toric surfaces

Cited by in corpus (1)

• Multiplier ideal sheaves and geometric problems