Research Article

Volume Inequalities and Additive Maps of Convex Bodies

Dr. Franz E. Schustera1

a1 Forschungsgruppe Konvexe und Diskrete Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8–10/1046, A-1040 Wien, Austria. E-mail:


Analogues of the classical inequalities from the Brunn-Minkowski theory for rotation intertwining additive maps of convex bodies are developed. Analogues are also proved of inequalities from the dual Brunn-Minkowski theory for intertwining additive maps of star bodies. These inequalities provide generalizations of results for projection and intersection bodies. As a corollary, a new Brunn-Minkowski inequality is obtained for the volume of polar projection bodies.

(Received December 10 2005)

MSC 2000

  • Primary, 52A39


Dedicated to Prof. Rolf Schneider on the occasion of his 65th birthday.