The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits

Valentino Tosatti Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208 Ben Weinkove Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208 Xiaokui Yang Morningside Center of Mathematics, Institute of Mathematics, HCMS, CEMS, NCNIS, HLM, UCAS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Differential Geometry mathscidoc:2207.10002

American Journal of Mathematics, 140, (3), 653-698, 2018.6
We investigate the Kähler-Ricci flow on holomorphic fiber spaces whose generic fiber is a Calabi-Yau manifold. We establish uniform metric convergence to a metric on the base, away from the singular fibers, and show that the rescaled metrics on the fibers converge to Ricci-flat Kähler metrics. This strengthens previous work of Song-Tian and others. We obtain analogous results for degenerations of Ricci-flat Kähler metrics.
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@inproceedings{valentino2018the,
  title={The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits},
  author={Valentino Tosatti, Ben Weinkove, and Xiaokui Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220703153709101747526},
  booktitle={American Journal of Mathematics},
  volume={140},
  number={3},
  pages={653-698},
  year={2018},
}
Valentino Tosatti, Ben Weinkove, and Xiaokui Yang. The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits. 2018. Vol. 140. In American Journal of Mathematics. pp.653-698. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220703153709101747526.
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