Advertisement

Journal d’Analyse Mathématique

, Volume 36, Issue 1, pp 50–74 | Cite as

Uniform domains and the quasi-hyperbolic metric

  • F. W. Gehring
  • B. G. Osgood
Article

Keywords

Quasiconformal Mapping Schwarzian Derivative Injectivity Property Uniform Domain M6bius Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. V. Ahlfors,Quasiconformal reflections, Acta Math.109 (1963), 291–301.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    G. D. Anderson,Dependence on dimension of a constant related to the Grötzsch ring, Proc. Amer. Math. Soc.61 (1976), 77–80.CrossRefMathSciNetGoogle Scholar
  3. 3.
    P. Caraman,n-Dimensional Quasiconformal (QCf) Mappings, Abacus Press, Tunbridge Wells, England, 1974.MATHGoogle Scholar
  4. 4.
    P. L. Duren, H. S. Shapiro and A. L. Shields,Singular measures and domains not of Smirnow type. Duke Math. J.33 (1966), 247–254.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    F. W. Gehring,Rings and quasiconformal mappings in space, Trans. Amer. Math. Soc.103 (1962), 353–393.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    F. W. Gehring and B. P. Palka,Quasiconformally homogeneous domains, J. Analyse Math.30 (1976), 172–199.MATHMathSciNetGoogle Scholar
  7. 7.
    E. Hille,Ordinary Differential Equations in the Complex Domain, John Wiley and Sons, New York, 1976.MATHGoogle Scholar
  8. 8.
    P. W. Jones,Extension theorems for BMO, Indiana Univ. Math. J.29 (1980), 41–66.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    O. Lehto,Quasiconformal Mappings in the Plane, Univ. of Maryland Lecture Notes14, 1975.Google Scholar
  10. 10.
    O. Lehto and K. I. Virtanen,Quasiconformal Mappings in the Plane, Springer-Verlag, New York, 1973.MATHGoogle Scholar
  11. 11.
    O. Martio,Definitions for uniform domains, Ann. Acad. Sci. Fenn. (to appear).Google Scholar
  12. 12.
    O. Martio and J. Sarvas,Injectivity theorems in plane and space, Ann. Acad. Sci. Fenn. (to appear).Google Scholar
  13. 13.
    G. D. Mostow,Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms, Inst. Hautes Études Sci. Publ. Math.34 (1968), 53–104.MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Z. Nehari,The Schwarzian derivative and schlicht functions, Bull. Amer. Math. Soc.55 (1949), 545–551.MATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    B. G. Osgood,Univalence criteria in multiply-connected domains, Trans. Amer. Math. Soc. (to appear).Google Scholar
  16. 16.
    S. Rickman,Characterization of quasiconformal arcs, Ann. Acad. Sci. Fenn.395 (1966), 7–30.MathSciNetGoogle Scholar
  17. 17.
    G. E. Shilov and B. L. Gurevich,Integral, Measure and Derivative: A Unified Approach, Prentice-Hall, Englewood Cliffs, 1966.MATHGoogle Scholar
  18. 18.
    R. J. Sibner,Remarks on the Koebe Kreisnormierungsproblem, Comm. Math. Helv.43 (1968), 289–295.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University of Jerusalem 1979

Authors and Affiliations

  • F. W. Gehring
    • 1
  • B. G. Osgood
    • 1
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

Personalised recommendations