Isoperimetric inequalites and areas of projections in \(\mathbb{R}^ n\)
type: Item
instance of: scholarly article
title: Isoperimetric inequalites and areas of projections in \(\mathbb{R}^ n\)
zbMATH Open document ID: 0807.53064
DOI: 10.1007/BF01874659
author: V. Pereyra
published in: Acta Mathematica Hungarica
publication date: 1995-02-23T00:00:00Z
review text: Let \({\mathcal C}\) be the family of all smooth closed curves of given length \(L\) in \(\mathbb{R}^ n\), and, for each \(C \in {\mathcal C}\), let \[ A = {1 \over 2} \sum^ n_{j = 1} \sum^ n_{ k = 1} \varepsilon_{jk} A_{jk} \] be the sum of the projected areas \(A_{jk}\) onto all planes \(Ox_ j x_ k\) with an assigned index \(\varepsilon_{jk} \in \{- 1,0,1\}\) such that \(\varepsilon_{kj} = - \varepsilon_{jk}\). The authors determine the greatest value of \(| A |/L^ 2\) over \({\mathcal C}\) and they also find a curve \(C \in {\mathcal C}\) for which this value is attained.
Mathematics Subject Classification ID: 53C65
zbMATH DE Number: 575894
zbMATH Keywords: closed curves
zbMATH Keywords: length
zbMATH Keywords: projected areas
reviewed by: Wolfgang W. Breckner
MaRDI profile type: Publication
cites work: Q3876353
cites work: Q4039749
cites work: Q3908127
cites work: An inequality related to the isoperimetric inequality
cites work: The isoperimetric inequality
cites work: Über das isoperimetrische Problem im Raum von \(n\) Dimensionen
cites work: An isoperimetric inequality for closed curves convex in even-dimensional Euclidean spaces
description: scientific article; zbMATH DE number 575894