Curvature Estimates for the Continuity Method
Hosea Wondo
TL;DR
This paper derives curvature estimates for solutions of the continuity method on compact Kähler manifolds with semi-ample canonical bundles, adapting techniques from the Kähler-Ricci flow to this setting.
Contribution
It provides new curvature bounds for the continuity method on semi-ample canonical line bundles, extending previous work on the Kähler-Ricci flow.
Findings
Curvature estimates for long-time solutions on semi-ample canonical bundles
Curvature bounds for metrics on product manifolds
Extension of flow techniques to the continuity method
Abstract
We obtain curvature estimates for long time solutions of the continuity method on compact K\"ahler 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 K\"ahler-Ricci flow to this setup. As an application, we derive curvature bounds for general metrics on product manifolds.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Black Holes and Theoretical Physics