Abstract or Additional Information
The Willmore flow arises as the L2L^2L2-gradient flow of the Willmore energy which is itself given by the integrated squared mean curvature of the considered surface.
After a short introduction and review of known results on the Willmore flow of curves and closed surfaces, we discuss the existence of solutions to the Willmore flow of compact open surfaces immersed in Euclidean space subject to Navier boundary conditions.
We further study the elastic flow of planar networks composed of curves meeting in triple junctions. As a main result we obtain that starting from a suitable initial network the flow exists globally in time if the length of each curve remains uniformly bounded away from zero and if at least one angle at each triple junction stays uniformly bounded away from zero, π\piπ and 2π2\pi2π.
This talk is based on my recently submitted PhD thesis and includes joint work with H. Abels, H. Garcke and A. Pluda.