Skip to main content
SpringerLink
Log in

Dilatation estimates for quasiconformal extensions

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

LetD andD′ be ring domains inB n, withS n−1 as one boundary component, and let\(f:\bar D \to \bar D'\) be a homeomorphism which isK-quasiconformal inD and withf(S n−1)=S n−1. According to a result of Gehringf÷S n−1 admits an extension\(g:\bar B^n \to \bar B^n \) which is quasiconformal inB n. We find here an upper bound for the dilatation ofg in terms ofn, K, and modD.

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. F. W. Gehring,A remark on moduli of rings, Comment. Math. Helv.36 (1962), 42–46.

    Article  MathSciNet  Google Scholar 

  2. F. W. Gehring,Extension theorems for quasiconformal mappings in n-space, J. Analyse Math.19 (1967), 149–169.

    Article  MATH  MathSciNet  Google Scholar 

  3. F. W. Gehring,A remark on domains quasiconformally equivalent to a ball, Ann. Acad. Sci. Fenn. Ser. A I2 (1976), 147–155.

    MathSciNet  MATH  Google Scholar 

  4. F. W. Gehring,Inequalities for condensers, hyperbolic capacity, and extremal lengths, Michigan Math. J.18 (1971), 1–20.

    Article  MATH  MathSciNet  Google Scholar 

  5. J. Sarvas,Symmetrization of condensers in n-space, Ann. Acad. Sci. Fenn. Ser A I522 (1972), 1–44.

    MathSciNet  Google Scholar 

  6. J. Väisälä,Lectures on n-dimensional quasiconformal mappings, Lecture Notes in Mathematics229, Springer-Verlag, Berlin-Heidelberg-New York, 1971.

    MATH  Google Scholar 

  7. J. Väisälä,Modulus and capacity inequalities, Ann. Acad. Sci. Fenn. Ser. A I509 (1972), 1–14.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Helsinki, Helsinki, Finland

    Marjatta Näätänen

Authors
  1. Marjatta Näätänen
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was started during a visit to Université de Paris, financed by a cultural exchange program between France and Finland.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Näätänen, M. Dilatation estimates for quasiconformal extensions. Israel J. Math. 29, 346–356 (1978). https://doi.org/10.1007/BF02761172

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02761172

Keywords

Search

Navigation