Skip to main content
SpringerLink
Log in

Locally Quasi-Möbius Mappings on a Circle

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

We introduce the notion of a -normal family of continuous light mappings from a circle S into itself. We prove that any -normal Möbius invariant family of mappings from a circle S into itself consists of locally ω-quasi-Möbius mappings with the same distortion function ω. Bibliography: 10 titles.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. V. Ahlfors, Lectures on Quasiconformal Mappings, Am. Math. Soc., Providence, RI (2006).

  2. J. A. Kelingos, “Boundary correspondence under quasiconformal mappings,” Mich. Math. J 13, 235–249 (1966).

    Article  MATH  MathSciNet  Google Scholar 

  3. P. Tukia and J. Väisälä, “Quasisymmertic embeddings of metric spaces,” Ann. Acad. Sci. Fenn., Ser AI, Math. 5, 97–114 (1980).

    Article  MATH  Google Scholar 

  4. J. Heinonen, Lectures on Analysis on Metric Spaces, Springer, New York (2001).

    Book  MATH  Google Scholar 

  5. V. V. Aseev, “Quasisymmertic Embeddings and Naps, Restrictedly Distorting Modulus” pin Russian], Dep. VINITI 06.11.84, No. 3209-84, Novosibirsk (1984).

  6. J. Väisälä, “Quasimöbius maps,” J. Anal. Math. 44, 218–234 (1985).

    Article  MATH  Google Scholar 

  7. P. P. Belinskii, General Properties of Quasiconformal Mappings [in Russian], Nauka, Novosibirsk (1974).

  8. F. W. Gehring, “The Carathéodory convergence theorem for quasiconformal mappings in space,” Ann. Acad. Sci. Fenn., Ser A1 336/11 (1963).

  9. J. Väisälä, “Invariants for quasisymmetric, quasimöbius and bilipschitz maps,” J. Anal. Math. 50, 201–233 (1988).

    Article  MATH  Google Scholar 

  10. V. V. Aseev, “Convergence and stability of bounded modulus distortion mappings” [in Russian], Sib. Mat. Zh. 25, No. 1, 19–29 (1984); English transl.: Sib. Math. J. 25, No. 1, 15–23 (1984).

  11. V. V. Aseev, “Normal families of topological embeddings” [in Russian], Din. Splosh. Sredy No. 2, 32–42 (1968).

  12. I. Del Prete, M. Di Iorio, and L. Holá, “Graph convergence of set-valued maps and its relationship to other convergences,” J. Appl. Anal, 6, No. 2, 213–226 (2000).

    MATH  MathSciNet  Google Scholar 

  13. V. V. Aseev, “Quasi-symmetric embeddings” [in Russian], Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 75 (2000); English transl.: J. Math. Sci., New York 108, No. 3, 375–410 (2002).

  14. S. Stoilov, Theory of Functions of Complex Variables. Vol. 2 [in Russian], In. Lit., Moscow (1962).

  15. R. Engelking, General Topology, Heldermann, Berlin (1989).

    MATH  Google Scholar 

  16. K. Kuratowski Topology. Vol. I, Academic Press, New York etc. (1966).

  17. N. Bourbaki, Éléments de Mathématique. Topologie Générale I, Hermann, Paris (1971).

  18. O. Lehto and K. Virtanen, Quasikonforme Abbildungen, Springer, Berlin etc. (1965).

Download references

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, SB RAS 4, pr. Akad. Koptyuga, Novosibirsk, 630090, Russia

    V. V. Aseev & D. G. Kuzin

Authors
  1. V. V. Aseev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. G. Kuzin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. V. Aseev.

Additional information

Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 14, No. 1, 2014, pp. 3-18.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aseev, V.V., Kuzin, D.G. Locally Quasi-Möbius Mappings on a Circle. J Math Sci 211, 724–737 (2015). https://doi.org/10.1007/s10958-015-2628-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-015-2628-6

Keywords

Search

Navigation