Crystalline hexagonal curvature flow of networks: short-time, long-time and self-similar evolutions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909084691726336 |
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| author | Bellettini, Giovanni Kholmatov, Shokhrukh Almuratov, Firdavsjon |
| author_facet | Bellettini, Giovanni Kholmatov, Shokhrukh Almuratov, Firdavsjon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15358 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Crystalline hexagonal curvature flow of networks: short-time, long-time and self-similar evolutions Bellettini, Giovanni Kholmatov, Shokhrukh Almuratov, Firdavsjon Analysis of PDEs Classical Analysis and ODEs Differential Geometry 53E10, 47H10, 35D35, 74E15 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. |
| title | Crystalline hexagonal curvature flow of networks: short-time, long-time and self-similar evolutions |
| topic | Analysis of PDEs Classical Analysis and ODEs Differential Geometry 53E10, 47H10, 35D35, 74E15 |
| url | https://arxiv.org/abs/2401.15358 |