## Abstract

In this paper we prove a compactness result for compact Kähler Ricci gradient shrinking solitons. If (M_{i}, g_{i}) is a sequence of Kähler Ricci solitons of real dimension n ≥ 4, whose curvatures have uniformly bounded L^{n / 2} norms, whose Ricci curvatures are uniformly bounded from below and μ (g_{i}, 1 / 2) ≥ A (where μ is Perelman's functional), there is a subsequence (M_{i}, g_{i}) 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 language | English (US) |
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Pages (from-to) | 794-818 |

Number of pages | 25 |

Journal | Advances in Mathematics |

Volume | 211 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 2007 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)

## Keywords

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