Positively curved shrinking Ricci solitons are compact

Abstract

We show that a shrinking Ricci soliton with positive sectional curvature must be compact. This extends a result of Perelman in dimension three and improves a result of Naber in dimension four, respectively.

submitted

References in corpus (1)

• Ricci flow with surgery on three-manifolds

Cited by in corpus (2)

• A compactness theorem for four-dimensional shrinking gradient Ricci solitons
• Remarks on shrinking gradient Kähler-Ricci solitons with positive bisectional curvature