The Collapsing Rate of the Kahler-Ricci Flow with Regular Infinite Time Singularity

Frederick Tsz-Ho Fong HKUST Zhou Zhang Sydney University

Differential Geometry mathscidoc:1703.10003

Distinguished Paper Award in 2018

J. Reine Angew. Math., 703, 95-113, 2015
We study the collapsing behavior of the Kähler–Ricci flow on a compact Kähler manifold X admitting a holomorphic submersion inherited from its canonical bundle. We show that the flow metric degenerates at exactly the rate of e^{-t} as predicted by the cohomology information, and so the fibres collapse at the optimal rate. Consequently, it leads to some analytic and geometric extensions to the regular case of works by J. Song and G. Tian. Its applicability to general Calabi–Yau fibrations will also be discussed in local settings.
Kahler-Ricci flow, semi-ample, Calabi-Yau fibrations
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@inproceedings{frederick2015the,
  title={The Collapsing Rate of the Kahler-Ricci Flow with Regular Infinite Time Singularity},
  author={Frederick Tsz-Ho Fong, and Zhou Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170312221220645714660},
  booktitle={J. Reine Angew. Math.},
  volume={703},
  pages={95-113},
  year={2015},
}
Frederick Tsz-Ho Fong, and Zhou Zhang. The Collapsing Rate of the Kahler-Ricci Flow with Regular Infinite Time Singularity. 2015. Vol. 703. In J. Reine Angew. Math.. pp.95-113. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170312221220645714660.
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