A constructive proof of Kirszbraun's theorem
type: Item
instance of: scholarly article
title: A constructive proof of Kirszbraun's theorem
zbMATH Open document ID: 1221.47091
DOI: 10.1134/S000143460811014X
published in: Mathematical Notes
publication date: 2011-08-20T00:00:00Z
review text: In what follows by \(\mathcal{X}\) we denote an \(n\)-dimensional Euclidean, spherical or hyperbolic space. A \(PL\)-isometry \(\varphi:P\rightarrow X\) of a polytope \(P\) in \(\mathcal{X}\) is defined as a continuous map for which there exits a locally finite triangulation of \(P\) such that, for any simplex \(T\) from this triangulation, the restriction of \(\varphi\) to \(T\) is a motion. The authors prove that any weakly contractive map \(f\) on a finite set of point \(U\subseteq \mathcal{X}\) can be extended to a \(PL\)-isometry on the entire space.
reviewed by: Mircea Balaj
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 52A35
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 52B99
Mathematics Subject Classification ID: 57Q99
zbMATH DE Number: 5941757
zbMATH Keywords: PL-isometry
zbMATH Keywords: weakly contractive map
zbMATH Keywords: extension of maps
zbMATH Keywords: Kirszbraun's theorem
zbMATH Keywords: Helly's theorem
zbMATH Keywords: separable space
author: Arseniy Akopyan
author: Alexey S. Tarasov
MaRDI profile type: Publication
cites work: A Lipschitz Condition Preserving Extension for a Vector Function
cites work: Kirszbraun's theorem and metric spaces of bounded curvature
cites work: A Generalization of Theorems of Kirszbraun and Minty
cites work: Markov chains, Riesz transforms and Lipschitz maps
cites work: Q5341481
full work available at URL: s000143460811014x
OpenAlex ID: W2086157527
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description: scientific article; zbMATH DE number 5941757