A compactness result for Kähler Ricci solitons

Huai Dong Cao, N. Sesum

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

In this paper we prove a compactness result for compact Kähler Ricci gradient shrinking solitons. If (Mi, gi) is a sequence of Kähler Ricci solitons of real dimension n ≥ 4, whose curvatures have uniformly bounded Ln / 2 norms, whose Ricci curvatures are uniformly bounded from below and μ (gi, 1 / 2) ≥ A (where μ is Perelman's functional), there is a subsequence (Mi, gi) converging to a compact orbifold (M, g) with finitely many isolated singularities, where g is a Kähler Ricci soliton metric in an orbifold sense (satisfies a soliton equation away from singular points and smoothly extends in some gauge to a metric satisfying Kähler Ricci soliton equation in a lifting around singular points).

Original languageEnglish (US)
Pages (from-to)794-818
Number of pages25
JournalAdvances in Mathematics
Volume211
Issue number2
DOIs
StatePublished - Jun 1 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Convergence
  • Generalized Kähler Ricci soliton orbifold metric
  • Limit orbifold metric
  • Sequence of Kähler Ricci solitons

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