A local gap theorem for Ricci shrinkers
Abstract
We prove a local gap theorem for Ricci shrinkers, which states that if the local $\mu$-functional at scale $1$ on a large ball centered at the minimum point of the potential function is close enough to $0$, then the shrinker must be the flat gaussian shrinker. In relation to our result, Yokota [Yo09, Yo12] proved the same result assuming the global $\mu$-functional to be close enough to $0$. Our result shows an aspect of how the local geometry of a shrinker controls the global geometry, which is also discussed in [LW19, LW20, LW21].
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Mathematical Dynamics and Fractals
Geometry and complex manifolds
Publication details
- Journal / source
- Communications in Analysis and Geometry
- Publisher
- International Press of Boston
- Volume
- 34
- Issue
- 1
- Pages
- 257–279
- Publication date
- 1 January 2026
- Language
- EN