Geodesic
Holomorphic Mappings of the Hyperbolic Space into the Complex Euclidean Space and the Bloch Theorem
Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 446-458

Voir la notice de l'article provenant de la source Cambridge University Press

This paper is to study various properties of holomorphic mappings defined on the unit ball B in the complex euclidean space Cn with ranges in the space Cm. Furnishing B with the standard invariant Kähler metric and Cm with the ordinary euclidean metric, we define, for each holomorphic mapping f : B → Cm, a pair of non-negative continuous functions qf and Qf on B ; see § 2 for the definition.Let (Ω), Ω > 0, be the family of holomorphic mappings f : B → Cn such that Qf(z) ≦ Ω for all z ∈ B. (Ω) contains the family (M) of bounded holomorphic mappings as a proper subfamily for a suitable M > 0. 
Hahn, Kyong T. Holomorphic Mappings of the Hyperbolic Space into the Complex Euclidean Space and the Bloch Theorem. Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 446-458. doi: 10.4153/CJM-1975-053-0
@article{10_4153_CJM_1975_053_0,
     author = {Hahn, Kyong T.},
     title = {Holomorphic {Mappings} of the {Hyperbolic} {Space} into the {Complex} {Euclidean} {Space} and the {Bloch} {Theorem}},
     journal = {Canadian journal of mathematics},
     pages = {446--458},
     year = {1975},
     volume = {27},
     number = {2},
     doi = {10.4153/CJM-1975-053-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-053-0/}
}
TY  - JOUR
AU  - Hahn, Kyong T.
TI  - Holomorphic Mappings of the Hyperbolic Space into the Complex Euclidean Space and the Bloch Theorem
JO  - Canadian journal of mathematics
PY  - 1975
SP  - 446
EP  - 458
VL  - 27
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-053-0/
DO  - 10.4153/CJM-1975-053-0
ID  - 10_4153_CJM_1975_053_0
ER  - 
%0 Journal Article
%A Hahn, Kyong T.
%T Holomorphic Mappings of the Hyperbolic Space into the Complex Euclidean Space and the Bloch Theorem
%J Canadian journal of mathematics
%D 1975
%P 446-458
%V 27
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-053-0/
%R 10.4153/CJM-1975-053-0
%F 10_4153_CJM_1975_053_0

[1] 1. Anderson, J. M., Clunie, J., and Ch. Pommerenke, On Block functions and normal functions, J. Reine Angew Math. 270 (1974), 12–37. Google Scholar

[2] 2. Barth, T. J., Taut and tight complex manifolds, Proc. Amer. Math. Soc. 24 (1970), 429–431. Google Scholar

[3] 3. Hahn, K. T., The non-euclidean Pythagorean theorem with respect to the Bergman metric, Duke Math. J. 33 (1966), 523–534. Google Scholar

[4] 4. Hahn, K. T., Higher dimensional generalization of the Bloch constant and their lower bounds, Trans. Amer. Math. Soc. 179 (1973), 263–274. Google Scholar

[5] 5. Hahn, K. T., Quantitative Bloch's theorem for certain classes of holomorphic mappings of the ball into Pn(C) (to appear). Google Scholar

[6] 6. Kobayashi, S. and Nomizu, K., Foundations of differential geometry, Vol. 2 (Interscience, New York, 1969). Google Scholar

[7] 7. Kobayashi, S., Hyperbolic manifolds and holomorphic mappings (Marcel Dekker, New York, 1970). Google Scholar

[8] 8. Landau, E., Ûber die Blochsche Konstante und zwei verwandte Weltkonstanten, Math. Z. 30 (1920), 608–634. Google Scholar

[9] 9. Lehto, O. and Virtanen, K. J., Boundary behaviour and normal metvmorphic functions, Acta Math. 97 (1957), 47–65. Google Scholar

[10] 10. L∞k, K. H., Schwarz lemma and analytic invariants, Sci. Sinica 7 (1958), 453–504. Google Scholar

[11] 11. Seidel, W. and Walsh, J. L., On the derivative of functions analytic in the unit circle and their radii of univalence and of p-valence, Trans. Amer. Math. Soc. 52 (1942), 129–216. Google Scholar

[12] 12. Veech, W. A., A second course in complex analysis (Benjamin, New York, 1967). Google Scholar

[13] 13. Wu, H., Normal families of holomorphic mappings, Acta Math. 119 (1967), 193–233. Google Scholar

Cité par Sources :