Inequalities for mixed projection bodies

Author:

Lutwak Erwin

Abstract

Mixed projection bodies are related to ordinary projection bodies (zonoids) in the same way that mixed volumes are related to ordinary volume. Analogs of the classical inequalities from the Brunn-Minkowski Theory (such as the Minkowski, Brunn-Minkowski, and Aleksandrov-Fenchel inequalities) are developed for projection and mixed projection bodies.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference41 articles.

1. A. D. Aleksandrov, On the theory of mixed volumes of convex bodies. I: Extension of certain concepts in the theory of convex bodies, Mat. Sb. 2 (1937), 947-972. (Russian)

2. \bysame, On the theory of mixed volumes of convex bodies. II: New inequalities between mixed volumes and their applications, Mat. Sb. 2 (1937), 1205-1238. (Russian)

3. Zonoid theory and Hilbert’s fourth problem;Alexander, Ralph;Geom. Dedicata,1988

4. Estimating the sizes of convex bodies from projections;Betke, U.;J. London Math. Soc. (2),1983

5. A class of convex bodies;Bolker, Ethan D.;Trans. Amer. Math. Soc.,1969

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