The Willmore conjecture was proved by F.\ Marques and A.\ Neves in 2012. Since then we

know that the Clifford torus has the lowest Willmore energy among all tori in $\mathbb R^3$.

I will present results concerning immersed Klein bottles in $\mathbb R^n$ with low Willmore

energy, $n\geq 4$. For Klein bottles immersed in $\mathbb R^4$ it is known that there are three

distinct regular homotopy classes each one containing an embedding. I will explain that

one of these classes contains the embedded Klein bottle with lowest Willmore energy among

all immersed Klein bottles. This minimizer has Willmore energy less than $7\pi$ and there

is a conjecture which surface it actually is. In the other two regular homotopy classes the

lowest possible value of the Willmore energy is $8 \pi$. There are infinitely many embedded

Klein bottles attaining this infimum. The talk is based on joint work with Jonas Hirsch and

Patrick Breuning.

Posted in

Speaker:

Elena Mäder-Baumdicker
Affiliation:

KIT Karlsruhe
Date:

Tue, 2017-04-04 10:00 - 10:30
Location:

MPIM Lecture Hall
Parent event:

Young Women in Geometry