Homothetic covering of convex hulls of compact convex sets

Abstract. Let K be a compact convex set and m be a positive integer. The convering functional of K with respect to m is the smallest λ ∈ [0, 1] such that K can be covered by m translates of λK. Estimations of the covering functionals of convex hulls of two or more compact convex sets are presented. It is proved that, if a three-dimensional convex body K is the convex hull of two compact convex sets having no interior points, then the least number c(K) of smaller homothetic copies of K needed to cover K is not greater than 8 and c(K) = 8 if and only if K is a parallelepiped.

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