Abstract:

Let K be a convex body in Rn and M a simplex. Given volumes of the radial pth mean of convex bodies, if p≥n, then V(K)≥V(M); if -1<p≤n, then V(K)≤V(M). On the other hand, given volumes of convex bodies, if p≥n, then V(RpK)≤V(RpM); if -1

Key words: convex body; radial p-th mean body; simplex; radial function; the dual Quermassintegrals