On the families of successive radii and the sum of convex sets (Q464801)

The author points out inequalities satisfied by members of eight families of outer and inner radii already studied by \textit{U. Betke} and \textit{M. Henk} [Mathematika 39, No. 2, 247--257 (1992; Zbl 0759.52006)]. These inequalities relate the value taken on the Minkowski sum of two convex bodies in the \(n\)-dimensional Euclidean space to the values taken on the summands. Most of the relations are the best possible ones. The non existence of reverse inequalities for most radii under consideration is also shown.