The Kähler-Ricci flow on hirzebruch surfaces

Jian Song*, Ben Weinkove

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


We investigate the metric behavior of the Kähler-Ricci flow on the Hirzebruch surfaces, assuming the initial metric is invariant under a maximal compact subgroup of the automorphism group. We show that, in the sense of Gromov-Hausdorff, the flow either shrinks to a point, collapses to P1 or contracts an exceptional divisor, confirming a conjecture of Feldman-Ilmanen-Knopf. We also show that similar behavior holds on higher-dimensional analogues of the Hirzebruch surfaces.

Original languageEnglish (US)
Pages (from-to)141-168
Number of pages28
JournalJournal fur die Reine und Angewandte Mathematik
Issue number659
StatePublished - Oct 2011

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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