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Value distribution of quasiregular mappings

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

Keywords

  • Meromorphic Function
  • Counting Function
  • Defect Relation
  • Essential Singularity
  • Quasiregular Mapping

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References

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

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  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.

    CrossRef  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  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.

    CrossRef  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 

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© 1983 Springer-Verlag

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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

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

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