Geodesic
Some questions in the value distribution theory of holomorphic mappings, and complex variations
Sbornik. Mathematics, Tome 43 (1982) no. 2, pp. 275-285 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper we study the asymptotic properties of the order functions $T_q$, $q\in\overline{1,m}$, of holomorphic mappings $f\colon\mathbf C^m\to\mathbf C^n$ in terms of the complex variations of corresponding plurisubharmonic functions. We introduce a class of mappings for which we prove a quasisurjectivity theorem of Sokhotskii type and give the asymptotics of the order functions. Bibliography: 13 titles. 
@article{SM_1982_43_2_a6,
     author = {P. V. Degtar'},
     title = {Some questions in the value distribution theory of holomorphic mappings, and complex variations},
     journal = {Sbornik. Mathematics},
     pages = {275--285},
     year = {1982},
     volume = {43},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1982_43_2_a6/}
}
TY  - JOUR
AU  - P. V. Degtar'
TI  - Some questions in the value distribution theory of holomorphic mappings, and complex variations
JO  - Sbornik. Mathematics
PY  - 1982
SP  - 275
EP  - 285
VL  - 43
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1982_43_2_a6/
LA  - en
ID  - SM_1982_43_2_a6
ER  - 
%0 Journal Article
%A P. V. Degtar'
%T Some questions in the value distribution theory of holomorphic mappings, and complex variations
%J Sbornik. Mathematics
%D 1982
%P 275-285
%V 43
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1982_43_2_a6/
%G en
%F SM_1982_43_2_a6
P. V. Degtar'. Some questions in the value distribution theory of holomorphic mappings, and complex variations. Sbornik. Mathematics, Tome 43 (1982) no. 2, pp. 275-285. http://geodesic.mathdoc.fr/item/SM_1982_43_2_a6/

[1] Shabat B. V., Vvedenie v kompleksnyi analiz, t. II, Nauka, M., 1976 | MR

[2] Kharvi R., Golomorfnye tsepi i ikh granitsy, Mir, M., 1979 | MR

[3] Carlson J. A., “A moving lemma for the transcendental Bezout problem”, Ann. Math., 103 (1976), 305–330 | DOI | MR

[4] Carlson J. A., Griffiths P. A., The order functions for entire holomorphic mappings. Value Dustribution Theory, Marcel Dekker, New York, 1974 | MR

[5] Vitushkin A. G., O mnogomernykh variatsiyakh, Gostekhizdat, M., 1955

[6] Ivanov L. D., Variatsii funktsii i mnozhestv, Nauka, M., 1975 | MR

[7] Chern S. S., Levine H., Nirenberg L., “Intrinsic normes on complex manifold”, Global Analysis (papers in honour of K. Kodaira), Univ. of Tokyo Press, 1969, 119–139 | MR

[8] Bedford E., Taylor B. A., “The Dirichlet problem for a complex Monge–Ampere equation”, Invent. Math., 37 (1976), 1–44 | DOI | MR | Zbl

[9] Khadviger G., Lektsii ob ob'eme, ploschadi poverkhnosti i izoperimetrii, Nauka, M., 1966

[10] Buzeman G., Vypuklye poverkhnosti, Nauka, M., 1964 | MR

[11] Blyashke V., Differentsialnaya geometriya, M., 1935

[12] Griffiths P. A., King J., “Nevanlinna theory and holomorphic mappings between algebraic varieties”, Acta math., 130 (1973), 145–220 ; Matematika. Novoe v zarubezhnoi nauke, No 1, Mir, M., 1976 | DOI | MR | Zbl

[13] Cornalba M., Shiffman B., “A counterexample to the “Transcendental Berout Problem””, Ann. Math., 96 (1972), 402–406 | DOI | MR | Zbl