The parallel volume at large distances

The parallel volume of a body K at distance r is the volume of the set of all points whose distance from K is at most r. In this talk we will see that the difference of the parallel volume of the convex hull of a body and the parallel volume of the body itself grows at most at rate r^(d-3) as r tends to infinity, where d is the dimension of the surrounding space. Then we will examine, whether this is also true for non-Euclidean norms.