Über die j-ten Überdeckungsdichten konvexer Körper

Let for positive integers j, k, d and convex bodies K of Euclidean d-space E^d of dimension at least j V_{j, k} (K) denote the maximum of the intrinsic volumes V_j(C) of those convex bodies whose j-skeleton skel_j(C) can be covered with k translates of K. Then the j-th k-covering density θ_j,k (K) is the ratio k V_j(K)/V_j,k(K). In particular, θ_d,k refers to the case of covering the entire convex bodies C and the density is measured with respect to the volume while for j=d-1 the surface of the bodies C is covered and accordingly the density is measured with respect to the surface area. The paper gives the estimate {Mathematical expression} for the j-th k-covering density and some related results.