Mathematische Annalen

, Volume 293, Issue 1, pp 123–141

Schottky-Landau growth estimates fors-normal families of holomorphic mappings

  • M. G. Zaidenberg

Mathematics Subject Classification (1991)

32 32A17 32A22 32H15 32H20 32H25 32H30 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Al Aladro, G.: Applications of the Kobayashi metric to normal functions of several complex variables. Util. Math.31, 13–24 (1987)Google Scholar
  2. Ba Bagemihl, F.: Some boundary properties of normal functions bounded on nontangential arcs. Arch. Math.14, 399–406 (1963)Google Scholar
  3. Br Brody, R.: Compact manifolds and hyperbolicity. Trans. Am. Math. Soc235, 213–219 (1978)Google Scholar
  4. CaWi Campbell, D.M., Wickes, G.: Characterizations of normal meromorphic functions. In: Laine, J. et al. (eds.) Complex Analysis, Joensuu 1978. (Lect. Notes Math., vol. 747, pp. 55–72). Berlin, Heidelberg, New York: Springer 1979Google Scholar
  5. CiKr Cima, J.A., Krantz, S.G.: The Lindelöf principle and normal functions of several complex variables. Duke Math. J.50, 303–328 (1983)Google Scholar
  6. Do Dovbuš, P.V.: Boundary behavior of normal holomorphic functions of several complex variables. Sov. Math., Dokl.25, 267–270 (1982)Google Scholar
  7. Ea Eastwood, A.: A propos des variétés hyperboliques complètes. C.R. Acad. Sci. Ser. A280, 1071–1075 (1975)Google Scholar
  8. Fu Funahashi, K.: Normal holomorphic mappings and classical theorems of function theory. Nagoya Math. J.32, 89–104 (1984)Google Scholar
  9. Ga1 Gavrilov, V.I.: Boundary properties of functions meromorphic in the unit disc (in Russian). Dokl. Akad. Nauk SSSR151, 19–22 (1963)Google Scholar
  10. Ga2 Gavrilov, V.I.: Limits on continuous curves and sequences of points of meromorphic and generalized meromorphic functions in the unit disc (in Russian). I. Vest. Mosk. Univ., Ser. I., Mat-Mehan.1, 44–55 (1964); II. ibid. Vest. Mosk. Univ., Ser. I., Mat-Mehan.2, 30–36, (1964)Google Scholar
  11. Gau Gauthier, P.: A criterion or normality. Nagoya Math. j.32, 272–282 (1968)Google Scholar
  12. GiDo Gichev, V.V., Dobrovol'skii, S.M.: On some characteristic properties of Bloch functions. Sib. Math. J.28, 61–64 (1987)Google Scholar
  13. Gr Green, M.L.: The hyperbolicity of complement of 2n+1 hyperplanes in ℙ9, and related results. Proc. Am. Math. Soc.66, 109–113 (1977)Google Scholar
  14. Ha1 Hahn, K.T.: Asymptotic behavior of normal mappings of several complex variables. Can. J. Math.36, 718–746 (1984)Google Scholar
  15. Hay1 Hayman, W.K.: Meromorphic functions. Oxford: Oxford University Press 1964Google Scholar
  16. Hay2 Hayman, W.K.: Uniformly normal families. Lectures on functions of a complex variable, pp. 199–212. Ann Arbor: University of Michigan Press 1955Google Scholar
  17. He Hempel, J.: A. A precise bound in the theorems of Schottky and Picard. J. Lond. Math. Soc.21, 279–286 (1980)Google Scholar
  18. Jä Järvi, P.: An extension theorem for normal functions. Proc. Am. Math. Soc.103, 1171–1174 (1988)Google Scholar
  19. Je1 Jenkins, J.A.: On explicit bounds in Schottky's theorem. Can. J. Math.7, 76–82 (1955)Google Scholar
  20. Je2 Jenkins, J.A.: On explicit bounds in Landau's theorem. Can. J. Math.8, 423–425 (1956)Google Scholar
  21. JoKw Joeseph, J.E., Kwack, M.H.: Normal and Bloch mappings on hyperbolic manifolds pp. 1–21. (Preprint)Google Scholar
  22. KiKo Kiernan, P., Kobayashi, Sh.: Holomorphic mappings into projective space with lacunary hyperplanes. Nagoya Math. J.50, 199–216 (1973)Google Scholar
  23. Ki Kiernan, P.: Hyperbolically imbedded spaces and the big Picard theorem. Math. Ann.204, 203–209 (1973)Google Scholar
  24. Ko Kobayashi, Sh.: Hyperbolic manifolds and holomorphic mappings. New York: M. Dekker 1970Google Scholar
  25. KrMa Krantz, S.G., Ma, D.: Bloch functions on strongly pseudoconvex domains. Indiana Univ. Math. J.37, 145–163 (1988)Google Scholar
  26. La Landau, E.: Über eine Verallgemeinerung des Picardsche Satzes. Sitzungsber. Preuss. Akad. Wiss.8, 1118–1133 (1904)Google Scholar
  27. Lan Lange, L.H.: Sur les cercles de remplissage non-Euclidions. Ann. Sci. Norm. Supér.77, 257–280 (1960)Google Scholar
  28. Levi Lehto, O., Virtanen, K.I.: Boundary behavior and normal meromorphic functions. Acta. math.97, 47–65 (1957)Google Scholar
  29. Mo Montel, P.: Leçons sur les familles normales de fonctions analytiques et leurs applications. Paris 1927Google Scholar
  30. Mi Milloux, H.: Le théorème de M. Picard, suites de fonctions holomorphes, fonctions méromorphes et fonctions entières. J. Math. Pures Appl., IX. Ser.3, 345–401 (1924)Google Scholar
  31. Os1 Ostrovskii, I.V.: Generalization of the Tichmarsh convolution theorem and the complexvalued measures uniquely determined by their restrictions to a half-line. (Lect. Notes Math., vol. 1155, pp. 256–283). Berlin, Heidelberg, New York: Springer 1985Google Scholar
  32. Os2 Ostrovskii, I.V.: On a certain class of functions of bounded variation on a line determined by its values on the half-line (in Russian). Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova92, 220–229 (1979)Google Scholar
  33. Ro1 Royden, H.L.: Remarks on the Kobayashi metric. (Lect. Notes Math., vol. 185, pp. 125–137). Berlin, Heidelberg, New York: Springer 1971Google Scholar
  34. Ro2 Royden, H.L.: A criterion for the normality of a family of meromorphic functions. Ann. Acad. Sci. Fenn., Ser. AI10, 499–500 (1985)Google Scholar
  35. Sch Schottky, F.: Über den Picardschen Satz und die Borelschen Ungleichungen. Sitzungsber. Preuss. Akad. Wiss.8, 1244–1263 (1904)Google Scholar
  36. Za1 Zaidenberg, M.G.: Picard's theorem and hyperbolicity. Sib. Math. J.24, 858–867 (1983)Google Scholar
  37. Za2 Zaidenberg, M.G.: On some applications of hyperbolic analysis (in Russian). Kompleksnyi Analiz i Matem, pp. 29–38. Fizika, Tezisy Konferentssi. Krasnoyarsk: Institut Fiziki SO AN SSSR 1988.Google Scholar
  38. Za3 Zaidenberg, M.G.: Transcendental solutions of Diophantine equations. Funct. Anal. Appl.22, 322–324 (1988)Google Scholar
  39. Za4 Zaidenberg, M.G.: Criteria of hyperbolicity and families of curves (in Russian). Teor. Funkts., Funkts. Anal. Prilozh.52, 40–54 (1989)Google Scholar
  40. Za5 Zaidenberg, M.G.: Families of curves and hyperbolicity (in Russian). Teor. Funkts., Funkts. Anal. Prilozh.53, 26–43 (1990)Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • M. G. Zaidenberg
    • 1
  1. 1.Max-Planck-Institut für MathematikBonn 3Germany

Personalised recommendations