Migrating elastic flows
arXiv:2303.12516 · doi:10.1016/j.matpur.2024.02.003
Abstract
Huisken's problem asks whether there is an elastic flow of closed planar curves that is initially contained in the upper half-plane but `migrates' to the lower half-plane at a positive time. Here we consider variants of Huisken's problem for open curves under the natural boundary condition, and construct various migrating elastic flows both analytically and numerically.
17 pages, 10 figures