Israel Journal of Mathematics

, Volume 14, Issue 3, pp 309–316 | Cite as

Polar reciprocal convex bodies

  • H. Guggenheimer


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.


Convex Body Unique Minimum Minkowski Plane Symmetric Convex Symmetric Body 
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Copyright information

© Hebrew University 1973

Authors and Affiliations

  • H. Guggenheimer
    • 1
  1. 1.Polytechnic Institute of BrooklynBrooklynU.S.A.

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