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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2404.08349 |
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| _version_ | 1866917638285819904 |
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| author | Bruna, Joaquim Cufí, Julià Reventós, Agustí |
| author_facet | Bruna, Joaquim Cufí, Julià Reventós, Agustí |
| contents | We establish some relations between the perimeter, the area and the visual angle of a planar compact convex set. Our first result states that Crofton's formula is the unique universal formula relating the visual angle, length and area. After that we give a characterization of convex sets of constant width by means of the behaviour of its isotopic sets at infinity. Also for this class of convex sets we prove that the existence of an isotopic circle is enough to ensure that the considered set is a disc. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08349 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On some relations between the Perimeter, the Area and the Visual Angle of a Convex Set Bruna, Joaquim Cufí, Julià Reventós, Agustí Differential Geometry 52A15, 53C65 We establish some relations between the perimeter, the area and the visual angle of a planar compact convex set. Our first result states that Crofton's formula is the unique universal formula relating the visual angle, length and area. After that we give a characterization of convex sets of constant width by means of the behaviour of its isotopic sets at infinity. Also for this class of convex sets we prove that the existence of an isotopic circle is enough to ensure that the considered set is a disc. |
| title | On some relations between the Perimeter, the Area and the Visual Angle of a Convex Set |
| topic | Differential Geometry 52A15, 53C65 |
| url | https://arxiv.org/abs/2404.08349 |