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arXiv · 2401.15358

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

Giovanni Bellettini·Shokhrukh Kholmatov·Firdavsjon Almuratov
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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.

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Giovanni Bellettini, Shokhrukh Kholmatov, Firdavsjon Almuratov. 2024-01-27. Crystalline hexagonal curvature flow of networks: short-time, long-time and self-similar evolutions. https://arxiv.org/abs/2401.15358

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