Kahler-Ricci flow on stable Fano manifolds

Abstract

We study the Kahler-Ricci flow on Fano manifolds. We show that if the curvature is bounded along the flow and if the manifold is K-polystable and asymptotically Chow semistable, then the flow converges exponentially fast to a Kahler-Einstein metric.

19 pages

References in corpus (4)

• The Kähler-Ricci flow on surfaces of positive Kodaira dimension
• On the construction of Nadel multiplier ideal sheaves and the limiting behavior of the Ricci flow
• The Kähler-Ricci flow with positive bisectional curvature
• Kähler-Ricci flow on a toric manifold with positive first Chern class

Cited by in corpus (9)

• The Kahler-Ricci flow through singularities
• Kähler-Ricci flow, Kähler-Einstein metric, and K-stability
• Contracting exceptional divisors by the Kähler-Ricci flow
• Kahler-Einstein metrics on Fano surfaces
• Ricci flow on Orbifold
• Stability of Kähler-Ricci flow in the space of Kähler metrics
• Degenerate complex Monge-Ampère flows on strictly pseudoconvex domains
• Kähler Ricci flow with vanished Futaki invariant
• Multiplier ideal sheaves and geometric problems