Stability analysis for the anisotropic curve shortening flow of planar networks
Michael Gößwein, Matteo Novaga, Paola Pozzi · Partial Differential Equations and Applications · 2024
Abstract In this article we consider the anisotropic curve shortening flow for a planar network of three curves which meet at a triple junction. We show that the anisotropic energy fulfills a Łojasiewicz–Simon gradient inequality from which we derive a stability result for the evolution. Precisely, we show that, for initial data which are close to the energy minimizer, the flow exists globally and converges to the minimizer.