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Algebra i Analiz, 2010, Volume 22, Issue 5, Pages 140–153 (Mi aa1208)  

This article is cited in 10 scientific papers (total in 10 papers)

Research Papers

On intrinsic isometries to Euclidean space

A. Petrunin


Abstract: Compact metric spaces that admit intrinsic isometries to the Euclidean $d$-space are considered. Roughly, the main result states that the class of such spaces coincides with the class of inverse limits of Euclidean $d$-polyhedra.

Keywords: ontrinsic isometry, path isometry, Riemannian metric, polyhedron, pro-Euclidean space.

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English version:
St. Petersburg Mathematical Journal, 2011, 22:5, 803–812

Bibliographic databases:

Received: 10.02.2010

Citation: A. Petrunin, “On intrinsic isometries to Euclidean space”, Algebra i Analiz, 22:5 (2010), 140–153; St. Petersburg Math. J., 22:5 (2011), 803–812

Citation in format AMSBIB
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\paper On intrinsic isometries to Euclidean space
\jour Algebra i Analiz
\yr 2010
\vol 22
\issue 5
\pages 140--153
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\transl
\jour St. Petersburg Math. J.
\yr 2011
\vol 22
\issue 5
\pages 803--812
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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. Le Donne E., “Lipschitz and Path Isometric Embeddings of Metric Spaces”, Geod. Dedic., 166:1 (2013), 47–66  crossref  mathscinet  zmath  isi  scopus
    2. A. Petrunin, A. Yashinski, “Piecewise distance preserving maps”, St. Petersburg Math. J., 27:1 (2016), 155–175  mathnet  crossref  mathscinet  isi  elib
    3. Minemyer B., “Isometric Embeddings of Polyhedra Into Euclidean Space”, J. Topol. Anal., 7:4 (2015), 677–692  crossref  mathscinet  isi  scopus
    4. Kirchheim B., Spadaro E., Szekelyhidi Jr. Laszlo, “Equidimensional Isometric Maps”, Comment. Math. Helv., 90:4 (2015), 761–798  crossref  mathscinet  zmath  isi  scopus
    5. Benjamini I., Shamov A., “Bi-Lipschitz Bijections of Z”, Anal. Geom. Metr. Spaces, 3:1 (2015), 313–324  crossref  mathscinet  isi  scopus
    6. Minemyer B., “Approximating Continuous Maps By Isometries”, N. Y. J. Math., 22 (2016), 741–753  mathscinet  zmath  isi  elib
    7. Barry Minemyer, “Simplicial isometric embeddings of polyhedra”, Mosc. Math. J., 17:1 (2017), 79–95  mathnet  mathscinet
    8. Boronski J.P., Kupka J., “the Topology and Dynamics of the Hyperspaces of Normal Fuzzy Sets and Their Inverse Limit Spaces”, Fuzzy Sets Syst., 321 (2017), 90–100  crossref  mathscinet  zmath  isi  scopus
    9. Lytchak A. Wenger S., “Intrinsic Structure of Minimal Discs in Metric Spaces”, Geom. Topol., 22:1 (2018), 591–644  crossref  mathscinet  zmath  isi  scopus
    10. Lytchak A., Wenger S., “Isoperimetric Characterization of Upper Curvature Bounds”, Acta Math., 221:1 (2018), 159–202  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и анализ St. Petersburg Mathematical Journal
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