Extending Lipschitz functions via random metric partitions
type: Item
instance of: scholarly article
title: Extending Lipschitz functions via random metric partitions
zbMATH Open document ID: 1074.46004
author: James R. Lee
author: Assaf Naor
published in: Inventiones Mathematicae
publication date: 2005-04-14T00:00:00Z
review text: The method of stochastic metric decomposition is applied to a number of problems concerning the extension of Lipschitz functions. For example, it is shown that there is a universal constant \(C>0\) such that for every metric space \(X\) its absolute extendability constant \(ae(X)\) does not exceed \(C \log \lambda(X)\), where \(\lambda(X)\) (the doubling constant of \(X\)) is the infimum of those \(\lambda\) so that every ball in \(X\) can be covered by \(\lambda\) balls of half the radius. For \(n\)-point metric spaces, the asymptotic growth of \(ae(X)\) can be estimated from above by \(C\log n / \log \log n .\) (\(ae(X)\) is the infimum of those \(K>0\) such that for every metric space \(Y \supset X\) and for every metric space \(Z\), every Lipschitz function \(f : X \to Z\) can be extended to the whole of \(Y\) with a no more than \(K\) times bigger Lipschitz constant.)
reviewed by: Vladimir Kadets
Mathematics Subject Classification ID: 46B07
Mathematics Subject Classification ID: 46B09
Mathematics Subject Classification ID: 54C20
Mathematics Subject Classification ID: 26A16
Mathematics Subject Classification ID: 60D05
zbMATH DE Number: 2156039
zbMATH Keywords: extension of Lipschitz functions
zbMATH Keywords: metric space
zbMATH Keywords: metric tree
zbMATH Keywords: stochastic metric decomposition
MaRDI profile type: Publication
full work available at URL: s00222-004-0400-5
OpenAlex ID: W2106663623
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DOI: 10.1007/S00222-004-0400-5
description: scientific article; zbMATH DE number 2156039