Prof. Dr. Ernst Kuwert
Project leader
Albert-Ludwigs-Universität Freiburg im Breisgau
Telephone: +49 761 203-5585
Homepage: http://home.mathematik.uni-freiburg.de/k…
Project
22Willmore 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):
22Willmore 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):
22Willmore 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):
22Willmore 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):
22Willmore functional and Lagrangian surfaces25The Willmore energy of degenerating surfaces and singularities of geometric flows