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arXiv · 1702.04237

Minkowski additive operators under volume constraints

Judit Abardia-Evéquoz·Andrea Colesanti·Eugenia Saorín Gómez
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Abstract

We investigate Minkowski additive, continuous, and translation invariant operators $\Phi:\mathcal{K}^n\to\mathcal{K}^n$ defined on the family of convex bodies such that the volume of the image $\Phi(K)$ is bounded from above and below by multiples of the volume of the convex body $K$, uniformly in $K$. We obtain a representation result for an infinite subcone contained in the cone formed by this type of operators. Under the additional assumption of monotonicity or $SO(n)$-equivariance, we obtain new characterization results for the difference body operator.

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Judit Abardia-Evéquoz, Andrea Colesanti, Eugenia Saorín Gómez. 2017-02-14. Minkowski additive operators under volume constraints. https://arxiv.org/abs/1702.04237

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