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Restricted chord projection and affine inequalities

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Abstract

It is proved that if ∏*K is the polar projection body of a convex body K in R n, 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.

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Authors and Affiliations

  1. Mathematics Department, Wuhan Iron and Steel University, 430081, Wuhan, Hubei, P.R. China

    Zhang Gaoyong

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  1. Zhang Gaoyong
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Zhang, G. Restricted chord projection and affine inequalities. Geom Dedicata 39, 213–222 (1991). https://doi.org/10.1007/BF00182294

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  • DOI: https://doi.org/10.1007/BF00182294

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