Geometriae Dedicata

, Volume 39, Issue 2, pp 213–222

Restricted chord projection and affine inequalities

  • Zhang Gaoyong 

DOI: 10.1007/BF00182294

Cite this article as:
Zhang, G. Geom Dedicata (1991) 39: 213. doi:10.1007/BF00182294


It is proved that if ∏*K is the polar projection body of a convex body K in Rn, then the volumes of K and ∏*K satisfy the inequality
$$V(K)^{n - 1} V(\Pi *K) \geqslant \frac{{(2n)!}}{{n^n \left( {n!} \right)^2 }},$$
with equality if and only if K is a simplex. A new zonoid, called the mean zonoid, is defined and some inequalities which characterize the simplices are also proved.

Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • Zhang Gaoyong 
    • 1
  1. 1.Mathematics DepartmentWuhan Iron and Steel UniversityWuhanP.R. China

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