## Dr. Lynn Heller

### Project leader

Leibniz-Universität Hannover

E-mail: lynn.heller(at)math.uni-hannover.de

Telephone: +49 0511 762 3897

Homepage: http://service.ifam.uni-hannover.de/~geo...

## Publications within SPP2026

We show that the well-known family of $2$-lobed Delaunay tori $\;f^b\;$ in $\;S^3,\;$ parametrized by $\;b \in \mathbb R_{\geq1},\;$ uniquely minimizes the Willmore energy among all immersions from tori into $3$-space of conformal class $\;(a, b)\;$. As a corollary we obtain an alternate proof of the Willmore conjecture in $3$-space. This new strategy can be generalized to arbitrary codimensions provided a classification of isothermic constrained Willmore tori is possible and all $\;f^b\;$ remain stable in all codimensions.

**Related project(s):****16**Minimizer of the Willmore energy with prescribed rectangular conformal class