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math.DG2023
Short closed geodesics and the Willmore energy
Marius Müller, Fabian Rupp, Christian Scharrer
We prove a lower bound on the length of closed geodesics for spheres with Willmore energy below . The energy threshold is optimal and the inequality cannot be extended to surfa…
math.AP2023
A biharmonic analogue of the Alt-Caffarelli problem
Hans-Christoph Grunau, Marius Müller
We study a natural biharmonic analogue of the classical Alt-Caffarelli problem, both under Dirichlet and under Navier boundary conditions. We show existence, basic properties and $…