On the collapsing of Calabi-Yau manifolds and Kähler-Ricci flows

Yang Li, Valentino Tosatti

Research output: Contribution to journalArticlepeer-review


We study the collapsing of Calabi-Yau metrics and of Kähler-Ricci flows on fiber spaces where the base is smooth. We identify the collapsed Gromov-Hausdorff limit of the Kähler-Ricci flow when the divisorial part of the discriminant locus has simple normal crossings. In either setting, we also obtain an explicit bound for the real codimension-2 Hausdorff measure of the Cheeger-Colding singular set and identify a sufficient condition from birational geometry to understand the metric behavior of the limiting metric on the base.

Original languageEnglish (US)
JournalJournal fur die Reine und Angewandte Mathematik
StatePublished - 2023

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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