Metric Flips with Calabi Ansatz

Jian Song, Yuan Yuan

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


We study the limiting behavior of the Kähler-Ricci flow on ℙ(O ℙn ⊕ O ℙn(-1) ⊕(m+1)) for m, n ≥ 1, assuming the initial metric satisfies the Calabi symmetry. We show that the flow either shrinks to a point, collapses to ℙ n or contracts a subvariety of codimension m + 1 in the Gromov-Hausdorff sense. We also show that the Kähler-Ricci flow resolves a certain type of cone singularities in the Gromov-Hausdorff sense.

Original languageEnglish (US)
Pages (from-to)240-265
Number of pages26
JournalGeometric and Functional Analysis
Issue number1
StatePublished - Feb 2012
Externally publishedYes


  • Gromov-Hausdorff convergence
  • Kähler-Ricci flow
  • flip
  • small contraction

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology


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