Short closed geodesics and the Willmore energy
Abstract
We prove a lower bound on the length of closed geodesics for spheres with Willmore energy below $6 \pi$. The energy threshold is optimal and the inequality cannot be extended to surfaces of higher genus. Moreover, we discuss consequences for the injectivity radius.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Journal of Differential Geometry
- Publisher
- International Press of Boston
- Volume
- 132
- Issue
- 3
- Pages
- 429-459
- Publication date
- 11 February 2026
- Language
- EN