Skip to main content
SpringerLink
Log in

Extremal distance and quasiconformal reflection constants of domains in ℝN

  • Published:
Journal d’Analyse Mathematique Aims and scope

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

  • [A] L. V. Ahlfors,Lectures on Quasiconformal Mappings, Van Nostrand, Princeton, 1966.

    MATH  Google Scholar 

  • [BI] B. Bojarski and T. Iwaniec,Analytical foundations of the theory of quasiconformal mappings in ℝ n, Ann. Acad. Sci. Fenn. Ser. A I Math.8 (1983), 257–324.

    MathSciNet  MATH  Google Scholar 

  • [C] P. Caraman,Homeomorfisme cvasiconforme n-dimensionale, Bucuresti, 1968.

  • [G1] F. W. Gehring,Quasiconformal mappings, Complex Analysis and Its Applications, Int. Atomic Energy Agency, Vienna2 (1976), 213–268.

    Google Scholar 

  • [G2] F. W. Gehring,Rings and quasiconformal mappings in space, Trans. Am. Math. Soc.103 (1963), 353–393.

    Article  MathSciNet  Google Scholar 

  • [GM] F. W. Gehring and O. Martio,Quasiextremal distance domains and extension of quasiconformal mappings, J. Analyse Math.45 (1985), 181–206.

    Article  MATH  MathSciNet  Google Scholar 

  • [GV] F. W. Gehring and J. Väisälä,The coefficients of quasiconformality of domains in space, Acta Math.114 (1965), 1–70.

    Article  MATH  MathSciNet  Google Scholar 

  • [Ha] Kari Hag,Quasiconformal boundary correspondences and extremal mappings, Thesis, University of Michigan, Ann Arbor, Michigan, 1972.

    Google Scholar 

  • [HN] Kari Hag and Marjatta Näätänen,On the outer coefficient of quasiconformality of a cylindrical map of a convex dihedral wedge, Ann. Acad. Sci. Fenn. Ser. A I Math.5 (1980), 125–130.

    MathSciNet  MATH  Google Scholar 

  • [HV] Kari Hag and M. K. Vamanamurthy,The coefficients of quasiconformality of cones in n-space, Ann. Acad. Sci. Fenn. Ser. A I Math.3 (1977), 267–275.

    MathSciNet  MATH  Google Scholar 

  • [HK] D. A. Herron and P. Koskela,Quasiextremal distance domains and conformal mappings onto circle domains, Complex Variables15 (1990), 167–179.

    MATH  MathSciNet  Google Scholar 

  • [He] J. Hesse,A p-extremal length and p-capacity equality, Ark. Mat.13 (1975), 131–144.

    Article  MATH  MathSciNet  Google Scholar 

  • [J] P. W. Jones,Quasiconformal mappings and extendability of functions in Sobolev spaces, Acta Math.147 (1981), 71–88.

    Article  MATH  MathSciNet  Google Scholar 

  • [MS] O. Martio and J. Sarvas,Injectivity theorems in the plane and space, Ann. Acad. Sci. Fenn. Ser. A I Math.4 (1979), 383–401.

    MathSciNet  MATH  Google Scholar 

  • [M] V. G. Maz’ja,Sobolev Spaces, Springer-Verlag, Berlin, 1985.

    MATH  Google Scholar 

  • [RR] T. Rado and P. V. Reichelderfe,Continuous transformations in Analysis, Springer-Verlag, Berlin, 1955.

    MATH  Google Scholar 

  • [V] J. Väisälä,Lectures on n-dimensional quasiconformal mappings, Lecture Notes in Math., Vol. 229, Springer-Verlag, Berlin, 1971.

    MATH  Google Scholar 

  • [Y] S. Yang,QED domains and NED sets in ℝ n, Trans Am. Math. Soc.334 (1992), 97–120.

    Article  MATH  Google Scholar 

Download references

Author information

Author notes

  1. Shanshuang Yang

    Present address: Department of Mathematics, University of California, 90024, Los Angeles, CA, USA

Authors and Affiliations

  1. Department of Mathematics, The University of Michigan, 48109, Ann Arbor, MI, USA

    Shanshuang Yang

Authors
  1. Shanshuang Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported in part by grants from the U.S. National Science Foundation, the Institut Mittag-Leffler and the Alfred P. Sloan Foundation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yang, S. Extremal distance and quasiconformal reflection constants of domains in ℝN . J. Anal. Math. 62, 1–28 (1994). https://doi.org/10.1007/BF02835946

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02835946

Keywords

Search

Navigation