arxiv: 1207.7290 · v1 · pith:3SVXPDSQnew · submitted 2012-07-31 · 🧮 math.MG · math.DG· math.FA

Volume inequalities and additive maps of convex bodies

Franz E. Schuster This is my paper

classification 🧮 math.MG math.DGmath.FA

keywords bodiesinequalitiesadditivebrunn-minkowskimapsanaloguesconvexintertwining

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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.

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Volume inequalities and additive maps of convex bodies

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