2016
DOI: 10.48550/arxiv.1602.03438
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Minkowski valuations under volume constraints

Abstract: We provide a description of the space of continuous and translation invariant Minkowski valuations Φ : K n → K n for which there is an upper and a lower bound for the volume of Φ(K) in terms of the volume of the convex body K itself. Although no invariance with respect to a group acting on the space of convex bodies is imposed, we prove that only two types of operators appear: a family of operators having only cylinders over (n − 1)-dimensional convex bodies as images, and a second family consisting essentiall… Show more

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