# Minkowski valuations under volume constraints

@article{AbardiaEvequoz2016MinkowskiVU, title={Minkowski valuations under volume constraints}, author={J. Abardia-Ev'equoz and A. Colesanti and E. S. G'omez}, journal={arXiv: Metric Geometry}, year={2016} }

We provide a description of the space of continuous and translation invariant Minkowski valuations $\Phi:\mathcal{K}^n\to\mathcal{K}^n$ for which there is an upper and a lower bound for the volume of $\Phi(K)$ 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… CONTINUE READING

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