Degeneration of shrinking Ricci solitons

Abstract

Let $(Y,d)$ be a Gromov-Hausdorff limit of closed shrinking Ricci solitons with uniformly upper bounded diameter and lower bounded volume. We prove that off a closed subset of codimension at least 2, $Y$ is a smooth manifold satisfying a shrinking Ricci soliton equation.

16 pages

References in corpus (3)

• Space of Ricci flows (II)
• Compactness theorems of gradient Ricci solitons
• Bounding sectional curvature along a Kähler-Ricci flow