The continuity method on minimal elliptic Kähler surfaces

Abstract

We prove that, on a minimal elliptic Kähler surface of Kodaira dimension one, the continuity method introduced by La Nave and Tian in \cite{LT} starting from any initial Kähler metric converges in Gromov-Hausdorff topology to the metric completion of the generalized Kähler-Einstein metric on its canonical model constructed by Song and Tian in \cite{ST06}.

V3, small changes, accepted by International Mathematics Research Notices

References in corpus (2)

• Some discretizations of geometric evolution equations and the Ricci iteration on the space of Kahler metrics, I
• Bounding diameter of singular Kähler metric

Cited by in corpus (6)

• Relative volume comparison of Ricci Flow and its applications
• Collapsing behavior of Ricci-flat Kahler metrics and long time solutions of the Kahler-Ricci flow
• Diameter and Ricci curvature estimates for long-time solutions of the Kahler-Ricci flow
• Geometric estimates for complex Monge-Ampere equations
• Curvature Estimates for the Continuity Method
• The continuity equation, Hermitian metrics and elliptic bundles