Short simple geodesic loops on a 2-sphere
Abstract
The classic Lusternik–Schnirelmann theorem states that there are three distinct simple periodic geodesics on any Riemannian 2-sphere M M . It has been proven by Y. Liokumovich, A. Nabutovsky and R. Rotman that the shortest three such curves have lengths bounded in terms of the diameter d d of M M . We show that at any point p p on M M there exist at least two distinct simple geodesic loops (geodesic segments that start and end at p p ) whose lengths are respectively bounded by 8 d 8d and 14 d 14d .
Fields of Study & Subjects
Geophysics and Gravity Measurements
Scientific Research and Discoveries
Algebraic and Geometric Analysis
Publication details
- Journal / source
- Transactions of the American Mathematical Society
- Volume
- 379
- Issue
- 9
- Pages
- 6267–6296
- Publication date
- 1 May 2026
- Language
- EN