Willmore Klein Bottles

Elena Mader-Baumdicker, Karlsruhe Institute of Technology
Fine Hall 314

This talk is about immersed Klein bottles in Euclidean space with low Willmore energy. I will present an existence result of the minimizer of the Willmore energy among immersed Klein bottles of at least codimension two. A good candidate for the minimizer is already known. It is a minimal surface in the four-sphere. Furthermore, I will present results concerning the existence of embedded Klein bottles that are minimizers in their regular homotopy classes in Euclidean four-space. The above mentioned absolute minimizer is the minimizer of one of these three classes. It turns out that in the other two classes there are infinitely many distinct minimizers. They all have Willmore energy 8π and their oriented double covers are twistor holomorphic. This talk is based on joint work with Jonas Hirsch and Patrick Breuning.