Convergence of Kähler-Ricci flow on lower dimensional algebraic manifolds of general type

Abstract

In this paper, we prove that the $L^4$-norm of Ricci curvature is uniformly bounded along a Kähler-Ricci flow on any minimal algebraic manifold. As an application, we show that on any minimal algebraic manifold $M$ of general type and with dimension $n\le 3$, any solution of the normalized Kähler-Ricci flow converges to the unique singular Kähler-Einstein metric on the canonical model of $M$ in the Cheeger-Gromov topology.

References in corpus (6)

• Riemannian geometry of Kahler-Einstein currents
• Bounding scalar curvature for global solutions of the Kahler-Ricci flow
• Regularity of Kähler-Ricci flows on Fano manifolds
• Riemannian geometry of Kahler-Einstein currents II: an analytic proof of Kawamata's base point free theorem
• Geometric convergence of the Kähler-Ricci flow on complex surfaces of general type
• On the Kahler Ricci flow on projective manifolds of general type

Cited by in corpus (3)

• KAWA lecture notes on the Kähler-Ricci flow
• Local Sobolev Constant Estimate for Integral Ricci Curvature Bounds
• Globally Existing Kähler-Ricci Flows