The hanging chain problem with respect to a circle
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866929351669317632 |
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| author | López, Rafael |
| author_facet | López, Rafael |
| contents | Let $\s^1$ be a circle in Euclidean plane. We consider the problem of finding the shape of a planar curve which is an extremal of the potential energy that measures the distance to $\s^1$. We describe the shape of these curves distinguishing if the curves lie in the inside or outside of $\s^1$. We extend the problem for energies that are powers to the distance to $\s^1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12947 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The hanging chain problem with respect to a circle López, Rafael Differential Geometry 53A04, 49K05, 49J05 Let $\s^1$ be a circle in Euclidean plane. We consider the problem of finding the shape of a planar curve which is an extremal of the potential energy that measures the distance to $\s^1$. We describe the shape of these curves distinguishing if the curves lie in the inside or outside of $\s^1$. We extend the problem for energies that are powers to the distance to $\s^1$. |
| title | The hanging chain problem with respect to a circle |
| topic | Differential Geometry 53A04, 49K05, 49J05 |
| url | https://arxiv.org/abs/2405.12947 |