Almost isometries of balls
type: Item
instance of: scholarly article
title: Almost isometries of balls
zbMATH Open document ID: 1014.46053
author: Eva Kopecká
published in: Journal of Functional Analysis
publication date: 2002-07-08T00:00:00Z
review text: Let \(\ell^n_2\) denote \(\mathbb{R}^n\) with the canonical Euclidean norm and \(B\) its unit ball. Let \(f\) be a bi-Lipschitz mapping of \(B\) into \(\ell^n_2\). The shape of \(f(B)\) in the case when both Lipschitz constants are close to one is investigated in the paper. The author also constructs an example of a mapping \(f\) with both Lipschitz constants arbitrarily close to one and such that \(f\) has distance (in the supremum norm) at least one from every isometry. This shows that a quasi-isometry can be far from all isometries.
Mathematics Subject Classification ID: 46T20
Mathematics Subject Classification ID: 46B07
zbMATH DE Number: 1764705
zbMATH Keywords: bi-Lipschitz mapping
zbMATH Keywords: Kolmogorov width
zbMATH Keywords: isometry
zbMATH Keywords: quasi-isometry
zbMATH Keywords: rigid mapping
MaRDI profile type: Publication
full work available at URL: jfan.2001.3862
OpenAlex ID: W2094378811
cites work: Isometric approximation
cites work: Q4060144
cites work: Not too well differentiable Lipschitz isomorphisms
cites work: Rotation and strain
cites work: A remark on quasi-isometries
cites work: Isometries and almost isometries between spaces of continuous functions
cites work: Q3344608
cites work: Affine properties and injectivity of quasi-isometries
cites work: Q4767830
DOI: 10.1006/JFAN.2001.3862
description: scientific article; zbMATH DE number 1764705