On the complements of union of open balls and related set classes
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909229335445504 |
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| author | Longinetti, Marco Manselli, Paolo Venturi, Adriana |
| author_facet | Longinetti, Marco Manselli, Paolo Venturi, Adriana |
| contents | Let a $R$-body be a closed set, complement of union of open balls of radius $R$ in the Euclidean space. Properties generalizing similar ones for convex sets are proved for the family of $R$-bodies; properties for the family of sets supported by spheres of radius $R$ (extension of the supporting hyperplane to convex bodies) are investigated. Comparison of that family with the sets of reach $R$ and with the $R$-rolling sets are studied. New properties for the previous families are proved, by using the $R$-cones, generalization of the convex cones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15427 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the complements of union of open balls and related set classes Longinetti, Marco Manselli, Paolo Venturi, Adriana Metric Geometry 52A01, 52A30 Let a $R$-body be a closed set, complement of union of open balls of radius $R$ in the Euclidean space. Properties generalizing similar ones for convex sets are proved for the family of $R$-bodies; properties for the family of sets supported by spheres of radius $R$ (extension of the supporting hyperplane to convex bodies) are investigated. Comparison of that family with the sets of reach $R$ and with the $R$-rolling sets are studied. New properties for the previous families are proved, by using the $R$-cones, generalization of the convex cones. |
| title | On the complements of union of open balls and related set classes |
| topic | Metric Geometry 52A01, 52A30 |
| url | https://arxiv.org/abs/2406.15427 |