## 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…

## Project

**16**Minimizer of the Willmore energy with prescribed rectangular conformal class

## Publications within SPP2026

Starting at a saddle tower surface, we give a new existence proof of the Lawson surfaces ξm,k of high genus by deforming the corresponding DPW potential. As a byproduct, we obtain for fixed m estimates on the area of ξm,k in terms of their genus g=mk≫1.

Pages | 31 |

Link to preprint version |

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

We show that the homogeneous and the 2-lobe Delaunay tori in the 3-sphere provide the only isothermic constrained Willmore tori in 3-space with Willmore energy below 8π. In particular, every constrained Willmore torus with Willmore energy below 8π and non-rectangular conformal class is non-degenerated.

Pages | 19 |

Link to preprint version |

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

We show that the of 2-lobed Delaunay tori are stable as constrained Willmore surfaces in the 3-sphere.

Pages | 14 |

Link to preprint version |

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