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.

24 pages

References in corpus (3)

• The logarithmic Sobolev inequality along the Ricci flow
• Convergence of a Kähler-Ricci flow
• The compactness result for Kähler Ricci solitons

Cited by in corpus (2)

• Degeneration of Kahler-Ricci solitons on Fano manifolds
• Regularity of Kähler-Ricci flow