Stability analysis for the anisotropic curve shortening flow of planar networks
Analysis of PDEs
2023-10-10 v1 Differential Geometry
Abstract
In this article we study the anisotropic curve shortening flow for a planar network of three curves with fixed endpoints and which meet in a triple junction. We show that the anisotropic curvature energy fulfills a Lojasiewicz-Simon gradient inequality and use this knowledge to derive stability results for the flow. Precisely, in our main theorem we show that for any initial data, which are -close to a (local) energy minimizer, the flow exists globally and converges to a possibly different energy minimum.
Keywords
Cite
@article{arxiv.2310.05596,
title = {Stability analysis for the anisotropic curve shortening flow of planar networks},
author = {Michael Gößwein and Matteo Novaga and Paola Pozzi},
journal= {arXiv preprint arXiv:2310.05596},
year = {2023}
}