Inequalities involving integrals of polar-conjugate concave functions
type: Item
instance of: scholarly article
title: Inequalities involving integrals of polar-conjugate concave functions
zbMATH Open document ID: 0903.52007
DOI: 10.1007/BF01317315
published in: Monatshefte für Mathematik
publication date: 1999-01-05T00:00:00Z
full work available at URL: https://eudml.org/doc/178809
review text: An inequality of K. Mahler providing a lower bound for the product of the area of a plane convex figure and the area of its polar convex figure can be written in the form of integrals of polar-conjugate concave functions [see \textit{M. Meyer}, Monatsh. Math. 112, No. 4, 297-301 (1991; Zbl 0737.52002)]. The authors generalise this inequality for integrals of powers of polar-conjugate functions and use it to derive further inequalities for the product of volumes of a convex body \(K\) and the polar to \(K-z\) where \(z\) is the Santaló point of \(K\).
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 26B25
zbMATH DE Number: 1154522
zbMATH Keywords: concave function
zbMATH Keywords: polar set
zbMATH Keywords: inequality
zbMATH Keywords: polar-conjugate functions
zbMATH Keywords: volumes
zbMATH Keywords: convex body
zbMATH Keywords: Santaló point
author: Mathieu Meyer
author: Shlomo Reisner
reviewed by: Ilya S. Molchanov
MaRDI profile type: Publication
cites work: Q4034370
cites work: Convex bodies with minimal volume product in \(\mathbb{R}^ 2\)
cites work: On the Blaschke-Santaló inequality
cites work: Q5287551
description: scientific article; zbMATH DE number 1154522