A width-diameter inequality for convex bodies

Erwin Lutwak

doi:10.1016/0022-247X(83)90231-7

A width-diameter inequality for convex bodies

Erwin Lutwak

Mathematics

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

Abstract

A special case of the Blaschke-Santaló inequality regarding the product of the volumes of polar reciprocal convex bodies is shown to be equivalent to a power-mean inequality involving the diameters and widths of a convex body. This power-mean inequality leads to strengthened versions of various known inequalities.

Original language	English (US)
Pages (from-to)	290-295
Number of pages	6
Journal	Journal of Mathematical Analysis and Applications
Volume	93
Issue number	1
DOIs	https://doi.org/10.1016/0022-247X(83)90231-7
State	Published - Apr 30 1983

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/0022-247X(83)90231-7

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title = "A width-diameter inequality for convex bodies",

abstract = "A special case of the Blaschke-Santal{\'o} inequality regarding the product of the volumes of polar reciprocal convex bodies is shown to be equivalent to a power-mean inequality involving the diameters and widths of a convex body. This power-mean inequality leads to strengthened versions of various known inequalities.",

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AB - A special case of the Blaschke-Santaló inequality regarding the product of the volumes of polar reciprocal convex bodies is shown to be equivalent to a power-mean inequality involving the diameters and widths of a convex body. This power-mean inequality leads to strengthened versions of various known inequalities.

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A width-diameter inequality for convex bodies

Abstract

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