Asymmetry of convex bodies of constant width
type: Item
instance of: scholarly article
title: Asymmetry of convex bodies of constant width
zbMATH Open document ID: 1242.52005
author: Qi Guo
author: Hai Lin Jin
published in: Discrete \& Computational Geometry
publication date: 2012-03-01T00:00:00Z
review text: The symmetry of convex bodies of constant width is discussed. It is shown that the Minkowski measure of asymmetry \(as_\infty (K)\) of an arbitrary convex body \(K\subset \mathbb{R}^n\) of constant width satisfies \(1\leq as_\infty(K)\leq \frac{n+\sqrt{2n(n+1)}}{n+2}\). The equality holds on the left-hand side if and only if \(K\) is an Euclidean ball. The upper bounds are attainable too: in particular, if \(n=3\), then the equality holds on the right-hand side if \(K\) is a Meissner body.
reviewed by: Anatoliy Milka
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 6010482
zbMATH Keywords: convex body of constant width
zbMATH Keywords: asymmetry measure
zbMATH Keywords: Meissner body
MaRDI profile type: Publication
full work available at URL: s00454-011-9370-8
OpenAlex ID: W1967118719
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DOI: 10.1007/S00454-011-9370-8
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description: scientific article; zbMATH DE number 6010482