Short closed geodesics and the Willmore energy
Differential Geometry
2026-02-16 v2
Abstract
We prove a lower bound on the length of closed geodesics for spheres with Willmore energy below . The energy threshold is optimal and the inequality cannot be extended to surfaces of higher genus. Moreover, we discuss consequences for the injectivity radius.
Keywords
Cite
@article{arxiv.2304.01809,
title = {Short closed geodesics and the Willmore energy},
author = {Marius Müller and Fabian Rupp and Christian Scharrer},
journal= {arXiv preprint arXiv:2304.01809},
year = {2026}
}
Comments
25 pages, 4 figures. New version contains explicit lower bound on the constant, independent of the codimension. To appear in J. Differential Geom