This is an announcement for the paper "Volume inequalities and additive maps of convex bodies" by Franz E. Schuster.

Abstract: 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.

Archive classification: math.MG math.DG math.FA

Mathematics Subject Classification: 52A40, 52A39

Citation: Mathematika 53 (2006), 211–234

Submitted from: franz.schuster@tuwien.ac.at

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1207.7290

or

http://arXiv.org/abs/1207.7290