Crystalline hexagonal curvature flow of networks: short-time, long-time and self-similar evolutions
Analysis of PDEs
2024-01-30 v1 Classical Analysis and ODEs
Differential Geometry
Abstract
We study the crystalline curvature flow of planar networks with a single hexagonal anisotropy. After proving the local existence of a classical solution for a rather large class of initial conditions, we classify the homothetically shrinking solutions having one bounded component. We also provide an example of network shrinking to a segment with multiplicity two.
Keywords
Cite
@article{arxiv.2401.15358,
title = {Crystalline hexagonal curvature flow of networks: short-time, long-time and self-similar evolutions},
author = {Giovanni Bellettini and Shokhrukh Kholmatov and Firdavsjon Almuratov},
journal= {arXiv preprint arXiv:2401.15358},
year = {2024}
}
Comments
45 pages, 23 figures