On isoperimetric inequalities in Minkowski spaces
type: Item
instance of: scholarly article
title: On isoperimetric inequalities in Minkowski spaces
zbMATH Open document ID: 1196.52007
DOI: 10.1155/2010/697954
author: Horst Martini
author: Zokhrab Mustafaev
published in: Journal of Inequalities and Applications
publication date: 2010-04-07T00:00:00Z
full work available at URL: https://eudml.org/doc/230699
review text: This paper gives a collection of isoperimetric-type inequalities involving convex bodies, their intersection and projection bodies, polars and Steiner symmetrals, and states some conjectures and open questions. It is shown how some of these inequalities are related to classic isoperimetric problems in Minkowski geometry. A large amount of background material is given, in the form of an overview of classical Euclidean isoperimetric problems, of the isoperimetric problem in finite-dimensional normed spaces, and sections on various notions from Minkowski geometry and convex geometry, including the Holmes-Thompson and Busemann area measures and their isoperimetrices.
reviewed by: Konrad J. Swanepoel
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52A21
zbMATH DE Number: 5689931
zbMATH Keywords: isoperimetric inequalities
zbMATH Keywords: Minkowski geometry
zbMATH Keywords: convex geometry
zbMATH Keywords: isoperimetrix
Wikidata QID: Q59254797
MaRDI profile type: Publication
OpenAlex ID: W2017908471
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