The kähler-ricci flow, ricci-flat metrics and collapsing limits

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7 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)653-698
Number of pages46
JournalAmerican Journal of Mathematics
Volume140
Issue number3
DOIs
StatePublished - Jun 2018

ASJC Scopus subject areas

  • Mathematics(all)

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