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Sibirsk. Mat. Zh., 2003, Volume 44, Number 6, Pages 1226–1238 (Mi smj1250)  

This article is cited in 13 scientific papers (total in 13 papers)

Linear bilipschitz extension property

P. Alestaloa, D. A. Trotsenkob, J. Vyaisyalyac

a Helsinki University of Technology
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
c University of Helsinki

Abstract: We give a sufficient geometric condition for a subset $A$ of $\mathbb{R}^n$ to enjoy the following property for a fixed $C\geqslant1$ There is $\delta>0$ such that for $0\leqslant\varepsilon\leqslant\delta$, each $(1+\varepsilon)$-bilipschitz map $f\colon A\to\mathbb{R}^n$ extends to a $(1+C\varepsilon)$-bilipschitz map $F\colon\mathbb{R}^n\to\mathbb{R}^n$.

Keywords: bilipschitz mapping, quasi-isometry, approximation, extension of mappings, subsets of euclidean space

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English version:
Siberian Mathematical Journal, 2003, 44:6, 959–968

Bibliographic databases:

UDC: 517.548.2
Received: 27.06.2003

Citation: P. Alestalo, D. A. Trotsenko, J. Vyaisyalya, “Linear bilipschitz extension property”, Sibirsk. Mat. Zh., 44:6 (2003), 1226–1238; Siberian Math. J., 44:6 (2003), 959–968

Citation in format AMSBIB
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\by P.~Alestalo, D.~A.~Trotsenko, J.~Vyaisyalya
\paper Linear bilipschitz extension property
\jour Sibirsk. Mat. Zh.
\yr 2003
\vol 44
\issue 6
\pages 1226--1238
\mathnet{http://mi.mathnet.ru/smj1250}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2034930}
\zmath{https://zbmath.org/?q=an:1063.30019}
\transl
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 6
\pages 959--968
\crossref{https://doi.org/10.1023/B:SIMJ.0000007471.47551.5d}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000187464000003}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kaenmaki A., Vilppolainen M., “Separation conditions on controlled Moran constructions”, Fundamenta Mathematicae, 200:1 (2008), 69–100  crossref  mathscinet  zmath  isi  scopus
    2. Alestalo P., Trotsenko D.A., “Plane Sets Allowing Bilipschitz Extensions”, Mathematica Scandinavica, 105:1 (2009), 134–146  crossref  mathscinet  zmath  isi  elib  scopus
    3. Diestel G., “Sobolev spaces with only trivial isometries, II”, Positivity, 13:4 (2009), 621–630  crossref  mathscinet  zmath  isi  scopus
    4. Xie X., “Quasiisometries between negatively curved Hadamard manifolds”, Journal of the London Mathematical Society–Second Series, 79:1 (2009), 15–32  crossref  mathscinet  zmath  isi  scopus
    5. D. A. Trotsenko, “Uniform domains close to a ball”, Siberian Math. J., 52:5 (2011), 937–950  mathnet  crossref  mathscinet  isi
    6. Trotsenko D.A., “Gromov Hyperbolic Discrete Spaces and Their Application to Extension of Classes of Mappings”, Doklady Mathematics, 83:3 (2011), 344–347  crossref  mathscinet  zmath  isi  elib  elib  scopus
    7. Trotsenko D.A., “Extendability of Classes of Maps and New Properties of Upper Sets”, Complex Anal Oper Theory, 5:3 (2011), 967–984  crossref  mathscinet  zmath  isi  elib  scopus
    8. Alestalo P., Trotsenko D.A., “On Mappings That Are Close to a Similarity”, Math. Rep., 15:4 (2013), 313–318  mathscinet  zmath  isi  elib
    9. D. A. Trotsenko, “An extendability condition for bilipschitz functions”, Siberian Math. J., 57:6 (2016), 1082–1087  mathnet  crossref  crossref  isi  elib
    10. Isabel Cortez M., Navas A., “Some Examples of Repetitive, Nonrectifiable Delone Sets”, Geom. Topol., 20:4 (2016), 1909–1939  crossref  mathscinet  zmath  isi  scopus
    11. Alestalo P., Trotsenko D.A., “on the Extension of Quasisymmetric Maps”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 41:2 (2016), 881–896  crossref  mathscinet  zmath  isi  scopus
    12. Mahabadi S., Makarychev K., Makarychev Yu., Razenshteyn I., “Nonlinear Dimension Reduction Via Outer Bi-Lipschitz Extensions”, Stoc'18: Proceedings of the 50Th Annual Acm Sigact Symposium on Theory of Computing, eds. Diakonikolas I., Kempe D., Henzinger M., Assoc Computing Machinery, 2018, 1088–1101  crossref  mathscinet  isi  scopus
    13. Kovalev L.V., “Symmetrization and Extension of Planar Bi-Lipschitz Maps”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 43:1 (2018), 541–556  crossref  mathscinet  zmath  isi  scopus
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