On two finite covering problems of Bambah,Rogers, Woods and Zassenhaus

Bambah, Rogers, Woods, and Zassenhaus considered the general problem of covering planar convex bodiesC byk translates of a centrally-symmetric convex bodyK ofE ² with the ramification that these translates cover the convex hullC _k of their centres. They proved interesting inequalities for the volume ofC andC _k . In the present paper some analogous results in euclideand-spaceE ^d are given. It turns out that on one hand extremal configurations ford5 are of quite different type than in the planar case. On the other hand inequalities similar to the planar ones seem to exist in general. Inequalities in both directions for the volume and other quermass-integrals are given.