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A characterization of the duality mapping for convex bodies

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Abstract.

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.

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Authors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13-15, H-1053, Budapest, Hungary

    Károly J. Böröczky

  2. Mathematisches Institut, Albert-Ludwigs-Universität, Eckerstr. 1, D-79104, Freiburg i. Br., Germany

    Rolf Schneider

Authors
  1. Károly J. Böröczky
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  2. Rolf Schneider
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Correspondence to Rolf Schneider.

Additional information

This work was supported by the EU-project DiscConvGeo (MTKD-CT-2005-014333). The first author was supported by OTKA grant 049301.

Received: March 2007, Accepted: April 2007

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Böröczky, K.J., Schneider, R. A characterization of the duality mapping for convex bodies. GAFA Geom. funct. anal. 18, 657–667 (2008). https://doi.org/10.1007/s00039-008-0676-5

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  • DOI: https://doi.org/10.1007/s00039-008-0676-5

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