Some results on the Willmore flow
speaker: Anna Dall'Acqua (Universität Ulm)abstract: In this talk we discuss some recent results on the Willmore flow. We first present a stricking relationship between Willmore surfaces of revolution and elastic curves in hyperbolic half-space. Here the term elastic curve refer to a critical point of the energy given by the integral of the curvature squared. In the talk we will discuss this relationship and use it to study long-time existence and asymptotic behavior for the L2-gradient flow of the Willmore energy, under the condition that the initial datum is a torus of revolution. As in the case of Willmore flow of spheres, we show that if an initial datum has Willmore energy below 8 \pi then the solution of the Willmore flow converges to the Clifford Torus, possibly rescaled and translated. The energy threshold of 8 \pi turns out to be optimal for such a convergence result.
Then, we present some results by Fabian Rupp on the Willmore flow for spheres with constant isoperimetric ratio. The lecture is based on joint work with M. Müller (Univ. Freiburg), R. Schätzle (Univ. Tübingen) and A. Spener (Univ. Ulm) and a preprint by Fabian Rupp (Univ. Wien).
timetable:
Thu 9 Jun, 16:30 - 17:30, Aula Dini
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