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Uspekhi Mat. Nauk, 2005, Volume 60, Issue 6(366), Pages 53–72 (Mi umn1676)  

This article is cited in 2 scientific papers (total in 2 papers)

Simultaneous Lipschitz extensions

A. Yu. Brudnyia, Yu. A. Brudnyib

a University of Calgary, Department of Mathematics and Statistics
b Technion – Israel Institute of Technology

Abstract: This paper is devoted to a study of a new bi-Lipschitz invariant $\lambda(M)$ of metric spaces $M$. Finiteness of this quantity means that the Lipschitz functions on any subset of $M$ can be linearly extended to functions on $M$ with Lipschitz constants increased by the factor $\lambda(M)$. It is shown that $\lambda(M)$ is finite for some important classes of metric spaces, including metric trees of any cardinality, groups of polynomial growth, hyperbolic groups in the Gromov sense, certain classes of Riemannian manifolds of bounded geometry, and finite direct sums of any combinations of these objects. On the other hand, an example is given of a two-dimensional Riemannian manifold $M$ of bounded geometry with $\lambda(M)=\infty$.

DOI: https://doi.org/10.4213/rm1676

Full text: PDF file (352 kB)
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English version:
Russian Mathematical Surveys, 2005, 60:6, 1057–1076

Bibliographic databases:

UDC: 517.988.22+517.51
MSC: Primary 26B35; Secondary 54E35, 46B15
Received: 30.09.2005

Citation: A. Yu. Brudnyi, Yu. A. Brudnyi, “Simultaneous Lipschitz extensions”, Uspekhi Mat. Nauk, 60:6(366) (2005), 53–72; Russian Math. Surveys, 60:6 (2005), 1057–1076

Citation in format AMSBIB
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\by A.~Yu.~Brudnyi, Yu.~A.~Brudnyi
\paper Simultaneous Lipschitz extensions
\jour Uspekhi Mat. Nauk
\yr 2005
\vol 60
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\pages 53--72
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\jour Russian Math. Surveys
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\vol 60
\issue 6
\pages 1057--1076
\crossref{https://doi.org/10.1070/RM2005v060n06ABEH004281}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33646406302}


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    This publication is cited in the following articles:
    1. St. Petersburg Math. J., 19:3 (2008), 397–406  mathnet  crossref  mathscinet  zmath  isi  elib
    2. Naor A., “Probabilistic Clustering of High Dimensional Norms”, Proceedings of the Twenty-Eighth Annual Acm-SIAM Symposium on Discrete Algorithms, Assoc Computing Machinery, 2017, 690–709  crossref  mathscinet  zmath  isi
  • Успехи математических наук Russian Mathematical Surveys
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