## Prof. Dr. Ernst Kuwert

### Project leader

Albert-Ludwigs-Universität Freiburg im Breisgau

E-mail: ernst.kuwert(at)math.uni-freiburg.de

Telephone: +49 761 203-5585

Homepage: http://home.mathematik.uni-freiburg.de/k…

## Project

**22**Willmore functional and Lagrangian surfaces

## Publications within SPP2026

We study immersed surfaces in R3 which are critical points of the Willmore functional under boundary constraints. The two cases considered are when the surface meets a plane orthogonally along the boundary, and when the boundary is contained in a line. In both cases we derive weak forms of the resulting free boundary conditions and prove regularity by reflection.

**Related project(s):****22**Willmore functional and Lagrangian surfaces

For the Willmore flow of spheres in R^n with small energy, we prove stability estimates for the barycenter, the quadratic moment, and in case n=3 also for the enclosed volume and averaged mean curvature. As applications, we give a new proof for a quasi-rigidity estimate due to De Lellis and Müller, also for an inequality by Röger and Schätzle for the isoperimetric deficit.

**Related project(s):****22**Willmore functional and Lagrangian surfaces

Let M be a compact Riemannian manifold which does not admit any immersed surface which is totally geodesic. We prove that then any completely immersed surface in M has area bounded in terms of the L^2 norm of the second fundamental form.

**Related project(s):****22**Willmore functional and Lagrangian surfaces

Journal | SIAM J. Math. Anal. |

Volume | 50 |

Pages | 4407--4425 |

Link to preprint version | |

Link to published version |

**Related project(s):****22**Willmore functional and Lagrangian surfaces**25**The Willmore energy of degenerating surfaces and singularities of geometric flows