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Israel Journal of Mathematics

, Volume 101, Issue 1, pp 73–84 | Cite as

On a method of Holopainen and Rickman

  • David Drasin
Article

Abstract

There exists a quasiregular map on ℝ n (n≥3) of finite order for which every ℝ n is an asymptotic value.

Keywords

Entire Function Meromorphic Function Finite Order Asymptotic Curve Analytic Entire Function 
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.

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References

  1. [1]
    D. Drasin,The inverse problem of the Nevanlinna theory, Acta Mathematica138 (1977), 83–151.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    D. Drasin and W.K. Hayman,Value distribution of functions meromorphic in an angle, Proceedings of the London Mathematical Society (3)48 (1984), 319–340.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    A. Eremenko,The set of asymptotic values of a meromorphic function of finite order (in Russian), Matematicheskie Zametki; English translation: Mathematical Notes24 (1979), 914–916.zbMATHMathSciNetGoogle Scholar
  4. [4]
    W. Gross,Eine ganz Funktion, für die jede komplexe Zahl Konvergenzwert ist, Mathematische Annalen79 (1918), 201–208.CrossRefMathSciNetGoogle Scholar
  5. [5]
    I. Holopainen and S. Rickman,The problem of the Denjoy theorem for quasiregular maps in dimension n≥3 Proceddings of the American Mathematical Society124 (1996), 1783–1788.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Yu. G. Reshetnyak,Space Mappings with Bounded Distortion (in Russian), Nauka, Moscow, 1982; English translation: Translations of Mathematical Monographs 73, American Mathematical Society, Providence, RI, 1989.Google Scholar
  7. [7]
    S. Rickman,Quasiregular Mappings, Ergebnisse der Mathematik (3) Band 26, Springer-Verlag, Berlin, 1993.zbMATHGoogle Scholar
  8. [8]
    S. Rickman and M. Vuorinen,On the order of quasiregular mappings, Annales Academicae Scientarum Fennicae, Series AI Mathematics7 (1982), 221–231.MathSciNetGoogle Scholar

Copyright information

© Hebrew University 1997

Authors and Affiliations

  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA

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