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arXiv · 2406.15427

On the complements of union of open balls and related set classes

Marco Longinetti·Paolo Manselli·Adriana Venturi
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Abstract

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.

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Marco Longinetti, Paolo Manselli, Adriana Venturi. 2024-05-22. On the complements of union of open balls and related set classes. https://arxiv.org/abs/2406.15427

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