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.

arXiv commentsubmitted

References in corpus (3)

• Ricci flow with surgery on three-manifolds
• Recent Progress on Ricci Solitons
• On Type I Singularities in Ricci flow

Cited by in corpus (5)

• Rigidity Theorem for integral pinched shrinking Ricci solitons
• Structure at infinity for shrinking Ricci solitons
• Hirzebruch manifolds and positive holomorphic sectional curvature
• A compactness theorem for four-dimensional shrinking gradient Ricci solitons
• Remarks on shrinking gradient Kähler-Ricci solitons with positive bisectional curvature