Premium
Volume Inequalities and Additive Maps of Convex Bodies
Author(s) -
Schuster Franz E.
Publication year - 2006
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300000103
Subject(s) - mixed volume , mathematics , convex body , minkowski space , intersection (aeronautics) , regular polygon , corollary , projection (relational algebra) , inequality , minkowski inequality , pure mathematics , convex geometry , mathematical analysis , convex set , geometry , convex hull , convex optimization , hölder's inequality , linear inequality , algorithm , engineering , aerospace engineering
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.