Collapsing of the Chern–Ricci flow on elliptic surfaces

Valentino Tosatti, Benjamin Weinkove*, Xiaokui Yang

*Corresponding author for this work

Research output: Contribution to journalArticle

18 Scopus citations

Abstract

We investigate the Chern–Ricci flow, an evolution equation of Hermitian metrics generalizing the Kähler–Ricci flow, on elliptic bundles over a Riemann surface of genus greater than one. We show that, starting at any Gauduchon metric, the flow collapses the elliptic fibers and the metrics converge to the pullback of a Kähler–Einstein metric from the base. Some of our estimates are new even for the Kähler–Ricci flow. A consequence of our result is that, on every minimal non-Kähler surface of Kodaira dimension one, the Chern–Ricci flow converges in the sense of Gromov–Hausdorff to an orbifold Kähler–Einstein metric on a Riemann surface.

Original languageEnglish (US)
Pages (from-to)1223-1271
Number of pages49
JournalMathematische Annalen
Volume362
Issue number3-4
DOIs
StatePublished - Dec 9 2015

Keywords

  • 32W20
  • 53C44
  • 53C55

ASJC Scopus subject areas

  • Mathematics(all)

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