Skip to main content
SpringerLink
Log in

Value distribution of quasiregular mappings

  • Conference paper
  • First Online:
Value Distribution Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 981))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ahlfors, L. V.: Zur Theorie der Überlagerunsflächen. Acta Math. 65 (1935), 157–194.

    Article  MathSciNet  MATH  Google Scholar 

  2. Drasin, D.: The inverse problem of the Nevanlinna Theory. Acta Math. 138 (1977), 83–151.

    Article  MathSciNet  MATH  Google Scholar 

  3. Granlund, S., Lindqvist, P., Martio, O.: Conformally invariant variational integrals. To appear.

    Google Scholar 

  4. Hinkkanen, A.: On the averages of the counting function of a meromorphic function. Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes 26 (1980), 1–31.

    MathSciNet  MATH  Google Scholar 

  5. Marden, A., Rickman, S.: Holomorphic mappings of bounded distortion. Proc. Amer. Math. Soc. 46 (1974), 226–228.

    Article  MathSciNet  MATH  Google Scholar 

  6. Martio, O., Rickman, S., Väisälä, J.: Definitions for quasiregular mappings. Ann. Acad. Sci. Fenn. Ser. A I Math. 448 (1969), 1–40.

    MathSciNet  MATH  Google Scholar 

  7. Martio, O., Rickman, S., Väisälä, J.: Distortion and singularities of quasiregular mappings. Ann. Acad. Sci. Fenn. Ser. A I Math. 465 (1970), 1–13.

    MathSciNet  MATH  Google Scholar 

  8. Martio, O., Rickman, S., Väisälä, J.: Topological and metric properties of quasiregular mappings. Ann. Acad. Sci. Fenn. Ser. A I Math. 488 (1971), 1–31.

    MATH  Google Scholar 

  9. Martio, O., Srebro, U.: On the existence of automorphic quasimeromorphic mappings in Rn. Ann. Acad. Sci. Fenn. Ser. A I Math. 3 (1977), 123–130.

    Article  MathSciNet  MATH  Google Scholar 

  10. Mattila, P., Rickman, S.: Averages of the counting function of a quasiregular mapping. Acta Math. 143 (1979), 273–305.

    Article  MathSciNet  MATH  Google Scholar 

  11. Miles, J.: On the counting function for the a-values of a meromorphic function. Trans. Amer. Math. Soc. 147 (1969), 203–222.

    MathSciNet  MATH  Google Scholar 

  12. Miles, J.: Bounds on the ratio n(r,a)/S(r) for meromorphic functions. Trans. Amer. Math. Soc. 162 (1971), 383–394.

    MathSciNet  MATH  Google Scholar 

  13. Nevanlinna, R.: Zur Theorie der meromorphen Funktionen. Acta Math. 46 (1925), 1–99.

    Article  MathSciNet  MATH  Google Scholar 

  14. Nevanlinna, R.: Analytic Functions. Springer-Verlag, Berlin-Heidelberg-New York (1970).

    Book  MATH  Google Scholar 

  15. Poleckii, E. A.: The modulus method for non-homeomorphic quasiconformal mappings (Russian). Mat. Sb. 83 (1970), 261–272.

    MathSciNet  Google Scholar 

  16. Rešetnjak, J. G.: Space mappings with bounded distortion (Russian). Sibirsk. Mat. Ž. 8 (1967), 629–658.

    MathSciNet  Google Scholar 

  17. Rešetnjak, J. G.: On the condition of the boundedness of index for mappings with bounded distortion (Russian). Sibirsk. Mat. Ž. 9 (1968), 368–374.

    MathSciNet  Google Scholar 

  18. Rešetnjak, J. G.: Extremal properties of mappings with bounded distortion (Russian). Sibirsk. Mat. Ž. 10 (1969), 1300–1310.

    MathSciNet  Google Scholar 

  19. Rickman, S.: Path lifting for discrete open mappings. Duke Math. J. 40 (1973), 187–191.

    Article  MathSciNet  MATH  Google Scholar 

  20. Rickman, S.: A quasimeromorphic mapping with given deficiencies in dimension three, in "Symposia Mathematica XVIII". Academic Press, London and New York, 535–543.

    Google Scholar 

  21. Rickman, S.: On the value distribution of quasimeromorphic maps. Ann. Acad. Sci. Fenn. Ser. A I Math. 2 (1976), 447–466.

    Article  MathSciNet  MATH  Google Scholar 

  22. Rickman, S.: Asymptotic values and angular limits of quasiregular mappings of a ball. Ann. Acad. Sci. Fenn. Ser. A I Math. 5 (1980), 185–196.

    Article  MathSciNet  MATH  Google Scholar 

  23. Rickman, S.: On the number of omitted values of entire quasiregular mappings. J. Analyse Math. 37 (1980), 100–117.

    Article  MathSciNet  MATH  Google Scholar 

  24. Rickman, S.: A defect relation for quasimeromorphic mappings. Ann. of Math. 114 (1981), 165–191.

    Article  MathSciNet  MATH  Google Scholar 

  25. Rickman, S.: Value distribution of quasimeromorphic mappings. To appear in Ann. Acad. Sci. Fenn. Ser. A I Math.

    Google Scholar 

  26. Tukia, P.: Automorphic quasimeromorphic mappings for torsionless hyperbolic groups. To appear.

    Google Scholar 

  27. Väisälä, J.: Lectures on n-Dimensional Quasiconformal Mappings. Lecture Notes in Mathematics 229, Springer-Verlag, Berlin-Heidelberg-New York (1971).

    MATH  Google Scholar 

  28. Väisälä, J.: Modulus and capacity inequalities for quasiregular mappings. Ann. Acad. Sci. Fenn. Ser. A I Math. 509 (1972), 1–14.

    Article  MATH  Google Scholar 

  29. Zorič, V. A.: The theorem of M. A. Lavrentiev on quasiconformal mappings in space (Russian). Mat. Sb. 74 (1967), 417–433.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Helsinki, 00100, Helsinki 10, Finland

    Seppo Rickman

Authors
  1. Seppo Rickman
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Ilpo Laine Seppo Rickman

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag

About this paper

Cite this paper

Rickman, S. (1983). Value distribution of quasiregular mappings. In: Laine, I., Rickman, S. (eds) Value Distribution Theory. Lecture Notes in Mathematics, vol 981. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066386

Download citation

  • DOI: https://doi.org/10.1007/BFb0066386

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12003-2

  • Online ISBN: 978-3-540-39480-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation