A note on Willmore minimizing Klein bottles in Euclidean space

Abstract

We show that Lawson's bipolar surface ${\tilde{\tau }}_{3,1}$ is after stereographic projection the unique minimizer among immersed Klein bottles in its conformal class. We conjecture that it actually is the unique minimizer among immersed Klein bottles into ${\mathbb{R}}^n$, $n\ge 4$, whose existence the authors and P. Breuning proved in a previous paper.

arXiv comment8 pages