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Polar reciprocal convex bodies

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An Erratum to this article was published on 01 June 1978

Abstract

The minimum of the product of the volume of a symmetric convex bodyK and the volume of the polar reciprocal body ofK relative to the center of symmetry is attained for the cube and then-dimensional crossbody. As a consequence, there is a sharp upper bound in Mahler’s theorem on successive minima in the geometry of numbers. The difficulties involved in the determination of the minimum for unsymmetricK are discussed.

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Authors and Affiliations

  1. Polytechnic Institute of Brooklyn, Brooklyn, N.Y., U.S.A.

    H. Guggenheimer

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  1. H. Guggenheimer
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Additional information

Reserch partially supported by NSF Grant GP-27960.

An erratum to this article is available at http://dx.doi.org/10.1007/BF02762019.

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Guggenheimer, H. Polar reciprocal convex bodies. Israel J. Math. 14, 309–316 (1973). https://doi.org/10.1007/BF02764893

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  • DOI: https://doi.org/10.1007/BF02764893

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