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On families of meromorphic maps into the complex projective space

Published online by Cambridge University Press:  22 January 2016

Hirotaka Fujimoto*
Affiliation:
Nagoya University
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In [10], P. Montel defined the notion of a quasinormal family of meromorphic functions and obtained several results relating to this. Afterwards, in [13], H. Rutishauser generalized some of them to the case of meromorphic functions of several variables. By definition, a quasi-normal family of meromorphic functions on a domain D in Cn is a family such that any sequence in has a subsequence which converges compactly outside a thin analytic subset of D.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1974

References

[1] Cartan, H., Sur les zéros des combinaisons linéaires de p fonctions holomorphes données, Mathematica, 7 (1933), 531.Google Scholar
[2] Drasin, D., Normal families and the Nevanlinna theory, Acta Math., 122 (1969), 231263.Google Scholar
[3] Dufresnoy, J., Théorie nouvelle des familles complexes normales; applications à l’étude des fonctions algebroïdes, Ann. E. N. S., (3) 61 (1944), 144.Google Scholar
[4] Fujimoto, H., On holomorphic maps into a taut complex space, Nagoya Math. J., 46 (1972), 4961.CrossRefGoogle Scholar
[5] Fujimoto, H., Extensions of the big Picard’s theorem, Tôhoku Math. J., 24 (1972), 415422.Google Scholar
[6] Fujimoto, H., Families of holomorphic maps into the projective space omitting some hyperplanes, J. Math. Soc. Japan 25 (1973), 235249.Google Scholar
[7] Fujimoto, H., On meromorphic maps into the complex projective space, J. Math. Soc. Japan, 26 (1974), 272288.Google Scholar
[8] Hayman, W. K., Meromorphic functions, Clarendon Press, Oxford, 1964.Google Scholar
[9] Kiernan, P. and Kobayashi, S., Holomorphic mappings into projective space with lacunary hyperplanes, Nagoya Math. J., 50 (1973), 199216.CrossRefGoogle Scholar
[10] Montel, P., Sur les familles quasi-normales de fonctions analytiques, Bull. Soc. Math., 52 (1924), 85114.Google Scholar
[11] Nishino, T., Sur les familles de surface analytiques, J. Math. Kyoto Univ., 1 (1962), 357377.Google Scholar
[12] Nishino, T., Sur une propriété des familles de fonctions analytiques de deux variables complexes, J. Math. Kyoto Univ., 4 (1965), 255282.Google Scholar
[13] Rutishauser, H., Über die Folgen und Scharen von analytischen und meromorphen Funktionen mehrerer variabeln, sowie von analytischen Abbildungen, Acta Math., 83 (1950), 249325.CrossRefGoogle Scholar
[14] Stoll, W., Die beiden Hauptsätze der Wertverteilungstheorie bei Funktionen mehrerer komplexen Veränderlichen (I), Acta Math., 90 (1953), 1115 and (II) Acta Math., 92 (1954), 55169.Google Scholar
[15] Stoll, W., The growth of the area of a transcendental analytic set I, Math. Ann., 156 (1964), 4778 and II, Math. Ann. 156 (1964), 144170.Google Scholar
[16] Stoll, W., Normal families of non-negative divisors, Math. Zeits., 84 (1964), 154218.Google Scholar
[17] Thullen, P., Über die wesentlichen Singularitäten analytischer Functionen und Flächen in Raum von n komplexen Veränderlichen, Math. Ann., 111 (1935), 137157.Google Scholar
[18] Valiron, G., Familles normales et quasi-normales de fonctions meromorphes, Mém. Sci. Math., Fasc. 38, 1929.Google Scholar