Degeneration of Kähler-Ricci solitons

Abstract

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.

arXiv comment24 pages

References in corpus (5)

• The logarithmic Sobolev inequality along the Ricci flow
• Space of Ricci flows (II)
• Compactness theorems of gradient Ricci solitons
• Convergence of a Kähler-Ricci flow
• The compactness result for Kähler Ricci solitons

Cited by in corpus (6)

• Degeneration of Kahler-Ricci solitons on Fano manifolds
• Regularity of Kähler-Ricci flows on Fano manifolds
• Regularity of Kähler-Ricci flow
• Compactness of Kahler-Ricci solitons on Fano manifolds
• New Volume Comparison results and Applications to degeneration of Riemannian metrics
• Existence of Kahler-Ricci solitons on smoothable Q-Fano varities