Higher-order estimates of long-time solutions to the Kähler-Ricci flow

Frederick Tsz Ho Fong, Man Chun Lee*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In this article, we study the higher-order regularity of the Kähler-Ricci flow on compact Kähler manifolds with semi-ample canonical line bundle. By developing sharp new parabolic Schauder estimates on cylinders, we proved that when the generic fibers of the Iitaka fibration are biholomorphic to each other, the flow converges in Cloc-topology away from singular fibers to a negative Kähler-Einstein metric on the base manifold. In particular, we proved that the Ricci curvature of the flow is uniformly bounded on any compact subsets away from singular fibers when the generic fibers are biholomorphic to each other.

Original languageEnglish (US)
Article number109235
JournalJournal of Functional Analysis
Issue number11
StatePublished - Dec 1 2021


  • Higher order regularity
  • Kahler-Ricci flow
  • Parabolic Schauder estimate
  • Semi-ample canonical line bundle

ASJC Scopus subject areas

  • Analysis


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