Calculus of Variations and Geometric Measure Theory

G. Bellettini - S. Kholmatov - F. Almuratov

Crystalline hexagonal curvature flow of networks: short-time, long-time and self-similar evolutions

created by kholmatov2 on 27 Jan 2024



Inserted: 27 jan 2024
Last Updated: 27 jan 2024

Year: 2024


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.

Tags: GeMeThNES
, GeoMeG
Keywords: crystalline curvature, anisotropy, network, partition, crystalline curvature flow