Optimizing geometric measures for fixed minimal annulus and inradius
type: Item
instance of: scholarly article
title: Optimizing geometric measures for fixed minimal annulus and inradius
zbMATH Open document ID: 1149.52009
DOI: 10.4171/RMI/520
author: Maria A. Hernández Cifre
author: Pedro J. Herrero-Piñeyro
published in: Revista Matemática Iberoamericana
publication date: 2008-05-29T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmi/1204128307
full work available at URL: https://eudml.org/doc/43622
review text: The aim of the authors is to investigate all possible and optimal relations stating the maximum and minimum values of the area, perimeter, diameter and the minimal width of a convex body, given its minimal annulus and its inradius. First, optimal upper and lower bounds of the area and perimeter of a convex body are given in terms of its circumradius and inradius. In particular, the case of a convex body with prescribed minimal annulus and inradius is taken into account. In the same manner, optimal upper and lower bounds for the diameter and the minimal width are approached. The corresponding extremal sets are determined for each optimal inequality.
reviewed by: Gabriela Cristescu
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 52A38
zbMATH DE Number: 5281237
zbMATH Keywords: convex body
zbMATH Keywords: minimal annulus
zbMATH Keywords: circumradius
zbMATH Keywords: inradius
zbMATH Keywords: area
zbMATH Keywords: perimeter
zbMATH Keywords: diameter
zbMATH Keywords: minimal width
MaRDI profile type: Publication
cites work: Q3797805
cites work: Q4753788
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OpenAlex ID: W2070489721
description: scientific article; zbMATH DE number 5281237