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Characterizing addition of convex sets by polynomiality of volume and by the homothety operation. (English) Zbl 1316.52004

/Addition/ is an associative and monotone operation on convex sets possessing a two-sided identity element. Except for Minkowski addition, the authors introduce a list of other additions and prove a number of characterization theorems. In particular, it is proven that Minkowski addition is the unique operation for convex sets for which the Minkowski theorem on polynomiality of the volume holds.

MSC:

52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
52A39 Mixed volumes and related topics in convex geometry
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