Remarks on Radial Centres of Convex Bodies

The paper concerns a family of selectors for convex bodies in Rn, radial centre maps, defined in the article of M. Moszynska, Looking for selectors of star bodies, Geom. Dedicata81 (2000), 131-147. A radial centre of a convex body A is the maximizer of a suitable generalized dual volume of A. We give physical interpretations of the notion of radial centre and study its geometric properties. We prove that these selectors are continuous with respect to the Hausdorff metric and solve the problem of direct additivity for radial centre of order α, which corresponds to the dual volume of order α