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This article is cited in 4 scientific papers (total in 4 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 $\lambda(M)=\infty$.
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
Linking options:
https://www.mathnet.ru/eng/rm1676https://doi.org/10.1070/RM2005v060n06ABEH004281 https://www.mathnet.ru/eng/rm/v60/i6/p53
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Abstract page: | 537 | Russian version PDF: | 275 | English version PDF: | 23 | References: | 50 | First page: | 1 |
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