Local Curvature Estimates of Long-Time Solutions to the Kahler-Ricci Flow

Frederick Tsz-Ho Fong Hong Kong University of Science and Technology Yashan Zhang Hunan University

Differential Geometry Geometric Analysis and Geometric Topology mathscidoc:2011.10001

Advances in Mathematics, 375, 107416, 2020.12
We study the local curvature estimates of long-time solutions to the normalized Kähler-Ricci flow on compact Kähler manifolds with semi-ample canonical line bundle. Using these estimates, we prove that on such a manifold, the set of singular fibers of the semi-ample fibration on which the Riemann curvature blows up at time-infinity is independent of the choice of the initial Kähler metric. Moreover, when a regular fiber of the semi-ample fibration is not a finite quotient of a torus, we determine the exact curvature blow-up rate of the Kähler-Ricci flow near the regular fiber.
Kahler-Ricci Flow, semi-ample canonical line bundle, singularity type, curvature estimates
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  title={Local Curvature Estimates of Long-Time Solutions to the Kahler-Ricci Flow},
  author={Frederick Tsz-Ho Fong, and Yashan Zhang},
  booktitle={Advances in Mathematics},
Frederick Tsz-Ho Fong, and Yashan Zhang. Local Curvature Estimates of Long-Time Solutions to the Kahler-Ricci Flow. 2020. Vol. 375. In Advances in Mathematics. pp.107416. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20201114033752033595723.
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