We investigate Minkowski additive, continuous, and translation invariant operators defined on the family of convex bodies such that the volume of the image is bounded from above and below by multiples of the volume of the convex body, uniformly. 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.
Minkowski additive operators under volume constraints / Judit, Abardia-evéquoz; Colesanti, Andrea; Eugenia, Saorìn-gòmez. - In: JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1559-002X. - ELETTRONICO. - 28:(2018), pp. 2422-2455. [10.1007/s12220-017-9909-x]
Minkowski additive operators under volume constraints
Andrea Colesanti
;
2018
Abstract
We investigate Minkowski additive, continuous, and translation invariant operators defined on the family of convex bodies such that the volume of the image is bounded from above and below by multiples of the volume of the convex body, uniformly. 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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