Firdavsjon Almuratov — Neckpinchhttps://neckpinch.com/authors/firdavsjon-almuratov/New arXiv papers by Firdavsjon Almuratov, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT Crystalline hexagonal curvature flow of networks: short-time, long-time and self-similar evolutionshttps://neckpinch.com/papers/2401.15358/arxiv:2401.15358Sat, 27 Jan 2024 00:00:00 GMTGiovanni Bellettini, Shokhrukh Kholmatov, Firdavsjon Almuratov — 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.Other curvature flowsAnisotropic & nonlocal flowsPhase fields & multiphase flows