Skip to main content
SpringerLink
Log in

Boundary regularity and the uniform convergence of quasiconformal mappings

  • Published:
Commentarii Mathematici Helvetici

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

References

  1. Courant, R.,Über eine Eigenschaft der Abbildungsfunktionen bei konformer Abbildung, Göttinger Nachr. (1922), 69–70.

  2. Gaier, D.,Über die konforme Abbildung veränderlicher Gebiete, Math. Z.64 (1965), 385–424.

    Article  MathSciNet  MATH  Google Scholar 

  3. Gehring, F. W.,The Carathéodory convergence theorem for quasiconformal mappings in space, Ann. Acad. Sci. Fenn. AI336/11 (1963), 1–21.

    MathSciNet  MATH  Google Scholar 

  4. Martio, O.,Equicontinuity theorem with an application to variational integrals, Duke Math. J.42 (1975), 569–581.

    Article  MathSciNet  MATH  Google Scholar 

  5. Näkki, R.,Continuous boundary extension of quasiconformal mappings, Ann. Acad. Sci. Fenn. AI511 (1972), 1–10.

    MATH  Google Scholar 

  6. —,Extension of Loewner's capacity theorem, Trans. Amer. Math. Soc.180 (1973), 229–236.

    MathSciNet  MATH  Google Scholar 

  7. Näkki, R.,Prime ends and quasiconformal mappings To appear in J. d'Analyse Math.

  8. Näkki, R. andPalka, B.,Uniform equicontinuity of quasiconformal mappings, Proc. Amer. Math. Soc.37 (1973), 427–433.

    Article  MathSciNet  MATH  Google Scholar 

  9. Palka, B.,Fréchet distance and the uniform convergence of quasiconformal mappings, Duke Math. J.39 (1972), 289–296.

    Article  MathSciNet  MATH  Google Scholar 

  10. —,On the uniform convergence of quasiconformal mappings, Trans. Amer. Math. Soc.184 (1973), 137–152.

    Article  MathSciNet  MATH  Google Scholar 

  11. Srebro, U., Conformal capacity and quasiconformal mappings in\(\bar R^n \) Israel J. Math.9 (1971), 93–110.

    Article  MathSciNet  MATH  Google Scholar 

  12. Väisälä, J.,Lectures on n-dimensional quasiconformal mappings, Lecture Notes in Math. 229, Springer-Verlag, Berlin-Heidelberg-New York, 1971.

    MATH  Google Scholar 

  13. Warschawski, S. E.,On the degree of variation in conformal mapping of variable regions, Trans. Amer. Math. Soc.69 (1950), 335–356.

    Article  MathSciNet  MATH  Google Scholar 

  14. Wilder, R. L.,Topology of manifolds, Amer. Math. Soc. Colloquium Ser. 32, Providence, 1949.

Download references

Author information

Authors and Affiliations

  1. University of Jyväskylä, Jyväskylä, Finland

    Raimo Näkki & Bruce Palka

  2. University of Texas, Austin, Texas, U.S.A.

    Raimo Näkki & Bruce Palka

Authors
  1. Raimo Näkki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bruce Palka
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Part of this research was done at the University of Michigan in 1974–75. The research was supported by the Academy of Finland.

This research was partially supported by NSF Grant MCS 76-06563.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Näkki, R., Palka, B. Boundary regularity and the uniform convergence of quasiconformal mappings. Commentarii Mathematici Helvetici 54, 458–476 (1979). https://doi.org/10.1007/BF02566287

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02566287

Keywords

Search

Navigation