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arXiv · 2304.01809

Short closed geodesics and the Willmore energy

Marius Müller·Fabian Rupp·Christian Scharrer
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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.

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Marius Müller, Fabian Rupp, Christian Scharrer. 2023-04-04. Short closed geodesics and the Willmore energy. https://doi.org/10.4310/jdg/1770825761

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