Kähler Ricci flow with vanished Futaki invariant

Abstract

We study the convergence of the Kähler-Ricci flow on a compact Kähler manifold $(M,J)$ with positive first Chern class $c_1(M;J)$ and vanished Futaki invariant on $\pi c_1(M;J)$. As the application we establish a criterion for the stability of the Kähler-Ricci flow (with perturbed complex structure) around a Kähler-Einstein metric with positive scalar curvature, under certain local stable condition on the dimension of holomorphic vector fields. In particular this gives a stability theorem for the existence of Kähler-Einstein metrics on a Kähler manifold with possibly nontrivial holomorphic vector fields.

23 pages; Remark 4.1 changed due to the comments of Valentino Tosatti

References in corpus (9)

• K-stability of constant scalar curvature Kähler manifolds
• Kähler-Ricci flow on a toric manifold with positive first Chern class
• Bounding sectional curvature along a Kähler-Ricci flow
• Compactness results for the Kähler-Ricci flow
• Stability of Kähler-Ricci flow
• Kähler Ricci flow on Fano surfaces (I)
• Kähler Ricci flow on Fano manifolds with vanished Futaki invariants
• Stability of Kähler-Ricci flow in the space of Kähler metrics
• Stability on Kähler-Ricci flow, I

Cited by in corpus (1)

• A compactness result for Fano manifolds and Kähler Ricci flows