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Algebra i Analiz, 2010, Volume 22, Issue 5, Pages 140–153 (Mi aa1208)  
This article is cited in 14 scientific papers (total in 14 papers)

Research Papers

On intrinsic isometries to Euclidean space

A. Petrunin
Full-text PDF (247 kB) Citations (14)
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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.
Received: 10.02.2010
English version:
St. Petersburg Mathematical Journal, 2011, Volume 22, Issue 5, Pages 803–812
DOI: https://doi.org/10.1090/S1061-0022-2011-01169-0
Bibliographic databases:
Document Type: Article
Language: Russian
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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Linking options:
  • https://www.mathnet.ru/eng/aa1208
  • https://www.mathnet.ru/eng/aa/v22/i5/p140
    • This publication is cited in the following 14 articles:
    1. Minemyer B., “The Isometric Embedding Problem For Length Metric Spaces”, J. Topol. Anal., 13:04 (2021), 889–932  crossref  mathscinet  isi
    2. Wasem M., “Equidimensional Isometric Extensions”, Z. Anal. ihre. Anwend., 40:3 (2021), 349–366  crossref  mathscinet  isi
    3. Creutz P., Soultanis E., “Maximal Metric Surfaces and the Sobolev-to-Lipschitz Property”, Calc. Var. Partial Differ. Equ., 59:5 (2020), 177  crossref  mathscinet  isi
    4. Petrunin A., Stadler S., “Metric-Minimizing Surfaces Revisited”, Geom. Topol., 23:6 (2019), 3111–3139  crossref  mathscinet  isi
    5. Lytchak A. Wenger S., “Intrinsic Structure of Minimal Discs in Metric Spaces”, Geom. Topol., 22:1 (2018), 591–644  crossref  mathscinet  zmath  isi  scopus
    6. Lytchak A., Wenger S., “Isoperimetric Characterization of Upper Curvature Bounds”, Acta Math., 221:1 (2018), 159–202  crossref  mathscinet  zmath  isi  scopus
    7. Barry Minemyer, “Simplicial isometric embeddings of polyhedra”, Mosc. Math. J., 17:1 (2017), 79–95  mathnet  crossref  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. Minemyer B., “Approximating Continuous Maps By Isometries”, N. Y. J. Math., 22 (2016), 741–753  mathscinet  zmath  isi  elib
    10. A. Petrunin, A. Yashinski, “Piecewise distance preserving maps”, St. Petersburg Math. J., 27:1 (2016), 155–175  mathnet  crossref  mathscinet  isi  elib
    11. Minemyer B., “Isometric Embeddings of Polyhedra Into Euclidean Space”, J. Topol. Anal., 7:4 (2015), 677–692  crossref  mathscinet  isi  scopus
    12. Kirchheim B., Spadaro E., Szekelyhidi Jr. Laszlo, “Equidimensional Isometric Maps”, Comment. Math. Helv., 90:4 (2015), 761–798  crossref  mathscinet  zmath  isi  scopus
    13. Benjamini I., Shamov A., “Bi-Lipschitz Bijections of Z”, Anal. Geom. Metr. Spaces, 3:1 (2015), 313–324  crossref  mathscinet  isi  scopus
    14. Le Donne E., “Lipschitz and Path Isometric Embeddings of Metric Spaces”, Geod. Dedic., 166:1 (2013), 47–66  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и анализ St. Petersburg Mathematical Journal
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