Bounding scalar curvature for global solutions of the Kahler-Ricci flow

Abstract

We show that the scalar curvature is uniformly bounded for the normalized Kahler-Ricci flow on a Kahler manifold with semi-ample canonical bundle. In particular, the normalized Kahler-Ricci flow has long time existence if and only if the scalar curvature is uniformly bounded, for Kahler surfaces, projective manifolds of complex dimension three, and for projective manifolds of all dimensions if assuming the abundance conjecture.

arXiv comment12 pages

References in corpus (3)

• The Kahler-Ricci flow through singularities
• A General Non-Vanishing Theorem and an Analytic Proof of the Finite Generation of the Canonical Ring
• Generalized Bergmann Metrics and Invariance of Plurigenera

Cited by in corpus (9)

• The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits
• Riemannian geometry of Kahler-Einstein currents
• Ricci flow and birational surgery
• Riemannian geometry of Kahler-Einstein currents II: an analytic proof of Kawamata's base point free theorem
• Convergence of Kähler-Ricci flow on lower dimensional algebraic manifolds of general type
• On the Kahler Ricci flow on projective manifolds of general type
• Geometric convergence of the Kähler-Ricci flow on complex surfaces of general type
• General Weak Limit for Kahler-Ricci Flow
• Globally Existing Kähler-Ricci Flows