On the complements of union of open balls and related set classes
Keywords:
generalized convexity, convex hull, rolling bodies, reach positive sets, support conesAbstract
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 sphere 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 ( G. Walther, On a generalization of Blachke's Rolling Theorem and the Smoothing Surfaces 1999) are studied. New properties for the previous familes are proved, by using the generalization of the convex cones.
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Copyright (c) 2026 Marco Longinetti, Paolo Manselli, Adriana Venturi
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