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).
All Science Journal Classification (ASJC) codes
- Generalized Kähler Ricci soliton orbifold metric
- Limit orbifold metric
- Sequence of Kähler Ricci solitons