Curvature Estimates for the Continuity Method

Abstract

We obtain curvature estimates for long time solutions of the continuity method on compact Kähler manifolds with semi-ample canonical line bundles. In this setting, initiated in arXiv:1410.3157 and arXiv:0709.0990, we adapt arguments from arXiv:1903.05939 for the Kähler-Ricci flow to this setup. As an application, we derive curvature bounds for general metrics on product manifolds.

arXiv commentCorrected errors in previous version

References in corpus (8)

• Some discretizations of geometric evolution equations and the Ricci iteration on the space of Kahler metrics, I
• The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits
• Collapsing of abelian fibred Calabi-Yau manifolds
• Infinite time singularities of the Kähler-Ricci flow
• Collapsing behavior of Ricci-flat Kahler metrics and long time solutions of the Kahler-Ricci flow
• The continuity method on minimal elliptic Kähler surfaces
• Geometry of twisted Kähler-Einstein metrics and collapsing
• Diameter and Ricci curvature estimates for long-time solutions of the Kahler-Ricci flow