The Lp‐diameter of the space of contractible loops
Abstract
Abstract We prove that the space of contractible simple loops of a given fixed area in any compact oriented surface has infinite diameter as a homogeneous space of the group of area‐preserving diffeomorphisms endowed with the ‐metric. As a special case, this resolves the ‐metric analog of the well‐known question in symplectic topology regarding the space of equators on the 2‐sphere. Our methods involve a new class of functionals on a normed group, which are more general than quasi‐morphisms.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Mathematical Dynamics and Fractals
Algebraic and Geometric Analysis
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 5
- Publication date
- 1 May 2026
- Language
- EN