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Ahlfors' theorem on asymptotic values and some developments from it

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1351)

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  • Entire Function
  • London Math
  • Quasiconformal Mapping
  • Subharmonic Function
  • Jordan Domain

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References

  1. L. V. Ahlfors, Untersuchungen zur Theorie der konformen Abbildungen und der ganzen Funktionen, Acta Soc. Sci. Fenn. Nova Ser. 1, No. 9 (1930).

    Google Scholar 

  2. T. Carleman, Sur une inégalité différentielle dans la théorie des fonctions analytiques, C. R. Acad. Sci. Paris 196 (1933), 995–997.

    MATH  Google Scholar 

  3. J. Clunie, On a paper of Kennedy, J. London Math. Soc. 33 (1958), 118–120.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. A. Denjoy, Sur les fonctions entières de genre fini, C. R. Acad. Sci. Paris 145 (1907), 106–108.

    MATH  Google Scholar 

  5. A. Denjoy, L'allure asymptotique des fonctions entières d'ordre fini, C. R. Acad. Sci. Paris 242 (1956), 213–218.

    MathSciNet  MATH  Google Scholar 

  6. B. G. Eke, Remarks on Ahlfors' distortion theorem, J. Analyse Math. 19 (1967), 97–134.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. P. C. Fenton, Entire functions having asymptotic functions, Bull. Austral. Math. Soc. 27 (1983), 321–328.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. S. Friedland and W. K. Hayman, Eigenvalue inequalities for the Dirichlet problem on spheres and the growth of subharmonic functions, Comment. Math. Helv. 51 (1976), 133–161.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. H. Grötzsch, Über einige Extremalprobleme der konformen Abbildung, Ber. sächs. Akad. Wiss. Leipzig, Math.-phys. K. 58 (1928), 367–376 and 497–502.

    Google Scholar 

  10. W. K. Hayman, On integral functions with distinct asymptotic values, Proc. Cambridge Phil. Soc. 66 (1969), 301–315.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. M. Heins, On the Denjoy-Carleman-Ahlfors theorem, Ann. of Math. 49 (1948), 533–537.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. M. Heins, On a notion of convexity connected with a method of Carleman, J. Analyse Math. 7 (1959), 53–77.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. J. A. Jenkins, On Ahlfors' spiral generalisation of the Denjoy conjecture, Indiana Univ. Math. J. 36 (1987), 41–44.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. W. Al-Katifi, On the asymptotic values and paths of certain integral and meromorphic functions, Proc. London Math. Soc. (3) 16 (1966), 599–634.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. P. B. Kennedy, A class of integral functions bounded on certain curves, Proc. London Math. Soc. (3) 6 (1956), 518–547.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. B. Kjellberg, On certain integral and harmonic functions: a study in minimum modulus, Thesis (Uppsala, 1948).

    Google Scholar 

  17. G. Somorjai, On asymptotic functions, J. London Math. Soc. (2) 21 (1980), 297–303.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. M. N. M. Talpur, On the sets, where a subharmonic funtion is large, Thesis (London, 1967), p. 155.

    Google Scholar 

  19. M. Tsuji, Potential theory in modern function theory, Maruzen, Tokyo, 1959.

    MATH  Google Scholar 

  20. A. Wiman, Sur une extension d'un théorème de M. Hadamard, Arkiv f. Mat., Astr. och Fys. 2, No. 14, 1905.

    Google Scholar 

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© 1988 Springer-Verlag

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Hayman, W.K. (1988). Ahlfors' theorem on asymptotic values and some developments from it. In: Laine, I., Sorvali, T., Rickman, S. (eds) Complex Analysis Joensuu 1987. Lecture Notes in Mathematics, vol 1351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081251

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  • DOI: https://doi.org/10.1007/BFb0081251

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50370-5

  • Online ISBN: 978-3-540-45992-7

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