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Volume Inequalities and Additive Maps of Convex Bodies

Part of: General convexity

Published online by Cambridge University Press:  21 December 2009

Franz E. Schuster
Franz E. Schuster
Affiliation:
Forschungsgruppe Konvexe und Diskrete Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8–10/1046, A-1040 Wien, Austria. E-mail: fschuster@osiris.tuwien.ac.at
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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.

MSC classification

Secondary: 52A39: Mixed volumes and related topics
Type
Research Article
Information
Mathematika , Volume 53 , Issue 2 , December 2006 , pp. 211 - 234
Copyright
Copyright © University College London 2006

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