Degeneration of Kähler-Ricci solitons

Gang Tian, Zhenlei Zhang

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Let (Y,d) be a Gromov-Hausdorff limit of n-dimensional closed shrinking Kähler-Ricci solitons with uniformly bounded volumes and Futaki invariants. We prove that off a closed subset of codimension at least 4, Y is a smooth manifold satisfying a shrinking Kähler-Ricci soliton equation. A similar convergence result for Kähler-Ricci flow of positive first Chern class is also obtained.

Original languageEnglish (US)
Pages (from-to)957-985
Number of pages29
JournalInternational Mathematics Research Notices
Issue number5
StatePublished - Jan 1 2012

All Science Journal Classification (ASJC) codes

  • General Mathematics


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