Short closed geodesics and the Willmore energy

2023/04/04 by Müller, Marius, Rupp, Fabian, Scharrer, Christian · 1 citation
#28A75 (secondary) #53A05 #53C22 (primary) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.01809

Abstract

We prove a lower bound on the length of closed geodesics for spheres with Willmore energy below 6π. The energy threshold is optimal and the inequality cannot be extended to surfaces of higher genus. Moreover, we discuss consequences for the injectivity radius.

Cited by

• The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow

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