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Volume inequalities and additive maps of convex bodies (1207.7290v1)
Published 31 Jul 2012 in math.MG, math.DG, and math.FA
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.