A characterization of the duality mapping for convex bodies

• DOI: 10.1007/s00039-008-0676-5
• Publication Date: 2008-08-02T07:54:28Z
• Authors: Károly J. Böröczky; Rolf Schneider
• Keywords: Duality (order theory); Characterization; Fenchel's duality theorem; Convex conjugate; Perturbation function

We characterize the duality of convex bodies in d-dimensional Euclidean vector space, viewed as a mapping from the space of convex bodies containing the origin in the interior into the same space. The question for such a characterization was posed by Vitali Milman. The property that the duality interchanges pairwise intersections and convex hulls of unions is sufficient for a characterization, up to a trivial exception and the composition with a linear transformation.