Geodesic
Deficient divisors in the Valiron sense
Sbornik. Mathematics, Tome 36 (1980) no. 4, pp. 535-547 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this article the author proves that for any holomorphic mapping $f\colon\mathbf C^n\to\mathbf P^m$ the set $$ E_V(f)=\biggl\{A\colon\varliminf_{r\to\infty}\frac{N_f(r,A)}{T_f(r)}<1\biggr\} $$ of hyperplanes deficient in the Valiron sense forms a polar set. This gives a positive answer to a question posed by Griffiths and King. Bibliography: 16 titles. 
@article{SM_1980_36_4_a5,
     author = {A. S. Sadullaev},
     title = {Deficient divisors in the {Valiron} sense},
     journal = {Sbornik. Mathematics},
     pages = {535--547},
     year = {1980},
     volume = {36},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1980_36_4_a5/}
}
TY  - JOUR
AU  - A. S. Sadullaev
TI  - Deficient divisors in the Valiron sense
JO  - Sbornik. Mathematics
PY  - 1980
SP  - 535
EP  - 547
VL  - 36
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1980_36_4_a5/
LA  - en
ID  - SM_1980_36_4_a5
ER  - 
%0 Journal Article
%A A. S. Sadullaev
%T Deficient divisors in the Valiron sense
%J Sbornik. Mathematics
%D 1980
%P 535-547
%V 36
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1980_36_4_a5/
%G en
%F SM_1980_36_4_a5
A. S. Sadullaev. Deficient divisors in the Valiron sense. Sbornik. Mathematics, Tome 36 (1980) no. 4, pp. 535-547. http://geodesic.mathdoc.fr/item/SM_1980_36_4_a5/

[1] P. Griffiths, J. King, “Nevanlinna theory and holomorphic mapping between algebraic varieties”, Acta Math., 130 (1973), 45–220 ; “Matematika”, Novoe v zarubezhnoi nauke, no. 1, izd-vo “Mir”, Moskva, 1976 | DOI | MR

[2] R. Nevanlinna, Odnoznachnye analiticheskie funktsii, Gostekhizdat, Moskva–Leningrad, 1941 | MR

[3] B. Shiftman, “Application of geometric measure theory to value distribution theory for meromorphic maps”, Value-Distr. theory, P. A.,, Marcel Dekker Inc., New York, 1974, 63–95 | MR

[4] M. Brelo, Osnovy klassicheskoi teorii potentsiala, izd-vo “Mir”, Moskva, 1964 | MR

[5] A. Sadullaev, Granichnaya teorema edinstvennosti v $\mathbf C^n$, Matem. sb., 101(143), 1976 | MR | Zbl

[6] J. Siciak, “Separately analytic functions and envelopes of holomorphy of some lower dimensional subsets of $\mathbf C^n$”, Ann. Polon Math., 22 (1969), 145–171 | MR | Zbl

[7] V. P. Zakharyuta, “Ekstremalnye plyurisubgarmonicheskie funktsii, gilbertovy shkaly i izomorfizm prostranstv analiticheskikh funktsii mnogikh peremennykh”, Teoriya funktsii, funktsionalnyi analiz, no. 19, Kharkov, 1974, 133–157 | Zbl

[8] P. belong, “Ensembles singuliers impropres des fonctions plurisous harmoniques”, J. Math., 36 (1957), 263–303 | MR

[9] P. Lelong, “Fonction plurisousharmoniques et fonctions analytiques reelles”, Ann. Inst. Fourier, Grenoble, 11 (1961), 515–562 | MR | Zbl

[10] P. Lelong, “Fonctions entieres ($n$ variables) et fonctions plurisousharmoniques de type exponentiel. Applications a l'analyse fonctionnelle”, Sovremennye problemy teorii analiticheskikh funktsii, izd-vo “Nauka”, Moskva, 1966, 188–209 ; | MR

[11] L. I. Ronkin, Vvedenie v teoriyu tselykh funktsii mnogikh peremennykh, izd-vo “Nauka”, Moskva, 1971 | MR

[12] B. V. Shabat, Vvedenie v kompleksnyi analiz, ch. II, izd-vo “Mir”, Moskva, 1976 | MR

[13] B. Josefson, “On the equivalence between locally polar and globally polar sets for plurisubharmonic functions in $\mathbf C^n$”, Arkiv Mat., 16:1 (1978), 109–115 | DOI | MR | Zbl

[14] V. P. Zakharyuta, “Transfinitnyi diametr, postoyannye Chebysheva i emkost dlya kompaktov v $\mathbf C^n$”, Matem. sb., 96(138) (1975), 374–389 | Zbl

[15] Chuang Chi-tai, “Une generalisation d'une inegalite de Nevanlinna”, Sci. Sinica, 13 (1964), 887–895 | MR | Zbl

[16] G. S. Prokopovich, “O nepodvizhnykh tochkakh meramorfnykh funktsii”, Ukr. matem. zh., 25:2 (1973), 248–260 | Zbl