On inner quermasses of convex bodies
type: Item
instance of: scholarly article
title: On inner quermasses of convex bodies
zbMATH Open document ID: 0637.52010
DOI: 10.1007/BF01194418
author: Horst Martini
published in: Archiv der Mathematik
publication date: 1989-01-01T00:00:00Z
review text: Let K be a convex body in \({\mathbb{R}}^ d\) (d\(\geq 3)\) and \b{V}\({}_{d- 1}(K,u)\) denote the inner (d-1)-quermass of K in direction u, i.e. the maximum area of the intersection of K and some hyperplane orthogonal to u. It is shown that \b{V}\({}_{d-1}(K,u)\) is smaller than or equal to the corresponding reciprocal value of the distance function of the projection body \(\Pi\) K of K. Moreover, the d-ellipsoids are characterized by equality for each direction. These relations imply elementary statements on the intersection body IK of K, which was recently introduced by E. Lutwak. Additionally, some unsolved problems concerning quermasses of convex bodies are formulated.
reviewed by: Horst Martini
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 4038641
zbMATH Keywords: ellipsoid
zbMATH Keywords: Blaschke-Santaló inequality
zbMATH Keywords: projection body
zbMATH Keywords: quermasses of convex bodies
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4038641