Restricted chord projection and affine inequalities

Gaoyong Zhang

doi:10.1007/BF00182294

Restricted chord projection and affine inequalities

Gaoyong Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 {Mathematical expression} 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.

Original language	English (US)
Pages (from-to)	213-222
Number of pages	10
Journal	Geometriae Dedicata
Volume	39
Issue number	2
DOIs	https://doi.org/10.1007/BF00182294
State	Published - Aug 1991

ASJC Scopus subject areas

Geometry and Topology

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10.1007/BF00182294

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abstract = "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 {Mathematical expression} 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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year = "1991",

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AB - 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 {Mathematical expression} 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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Restricted chord projection and affine inequalities

Abstract

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