Intermediate surface area measures and projection functions of convex bodies
type: Item
instance of: scholarly article
title: Intermediate surface area measures and projection functions of convex bodies
zbMATH Open document ID: 0813.52011
DOI: 10.1007/BF01193552
author: Christina Bauer
published in: Archiv der Mathematik
publication date: 1995-06-07T00:00:00Z
review text: It is proved that a convex polytopye in \(\mathbb{R}^ d\), whose faces satisfy a certain assumption of general position, is uniquely determined, up to translation or reflection, by its \(i\)th projection function if \(i\in \{2,\dots d-2\}\). For this, convex bodies in \(\mathbb{R}^ d\) whose \(i\)th area measure, \(i\in \{2,\dots, d-2\}\) is dominated by the sum of the \(i\)th area measures of two polytopes are investigated first. Also corresponding results for most convex bodies in terms of Baire category are studied.
Mathematics Subject Classification ID: 52B11
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 52A38
zbMATH DE Number: 734525
zbMATH Keywords: intermediate area measure
zbMATH Keywords: convex polytopye in \(\mathbb{R}^ d\)
zbMATH Keywords: projection function
zbMATH Keywords: convex bodies in \(\mathbb{R}^ d\)
zbMATH Keywords: Baire category
MaRDI profile type: Publication
cites work: Q5768387
cites work: Q4839521
cites work: Q5287551
description: scientific article; zbMATH DE number 734525