logo AFST
Uniqueness problem for meromorphic mappings with truncated multiplicities and few targets
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 15 (2006) no. 2, pp. 217-242.

Dans cet article, on donne un théorème d’unicité pour des applications méromorphes de m dans P n avec multiplicités coupées et avec « peu de » cibles. On donne aussi un théorème de dégénération linéaire pour des telles applications avec multiplicités coupées et avec des cibles mobiles. Les preuves utilisent des techniques de la distribution des valeurs.

In this paper, using techniques of value distribution theory, we give a uniqueness theorem for meromorphic mappings of m into P n with truncated multiplicities and “few" targets. We also give a theorem of linear degeneration for such maps with truncated multiplicities and moving targets.

DOI : 10.5802/afst.1120
Gerd Dethloff 1 ; Tran Van Tan 1

1 Université de Bretagne Occidentale, UFR Sciences et Techniques, Département de Mathématiques, 6, avenue Le Gorgeu, BP 452, 29275 Brest Cedex (France).
@article{AFST_2006_6_15_2_217_0,
     author = {Gerd Dethloff and Tran Van Tan},
     title = {Uniqueness problem for meromorphic mappings with truncated multiplicities and few targets},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {217--242},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 15},
     number = {2},
     year = {2006},
     doi = {10.5802/afst.1120},
     mrnumber = {2244216},
     zbl = {1111.32016},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1120/}
}
TY  - JOUR
AU  - Gerd Dethloff
AU  - Tran Van Tan
TI  - Uniqueness problem for meromorphic mappings with truncated multiplicities and few targets
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2006
SP  - 217
EP  - 242
VL  - 15
IS  - 2
PB  - Université Paul Sabatier, Institut de Mathématiques
PP  - Toulouse
UR  - https://afst.centre-mersenne.org/articles/10.5802/afst.1120/
DO  - 10.5802/afst.1120
LA  - en
ID  - AFST_2006_6_15_2_217_0
ER  - 
%0 Journal Article
%A Gerd Dethloff
%A Tran Van Tan
%T Uniqueness problem for meromorphic mappings with truncated multiplicities and few targets
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2006
%P 217-242
%V 15
%N 2
%I Université Paul Sabatier, Institut de Mathématiques
%C Toulouse
%U https://afst.centre-mersenne.org/articles/10.5802/afst.1120/
%R 10.5802/afst.1120
%G en
%F AFST_2006_6_15_2_217_0
Gerd Dethloff; Tran Van Tan. Uniqueness problem for meromorphic mappings with truncated multiplicities and few targets. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 15 (2006) no. 2, pp. 217-242. doi : 10.5802/afst.1120. https://afst.centre-mersenne.org/articles/10.5802/afst.1120/

[1] G. Dethloff; Tran Van Tan Uniqueness problem for meromorphic mappings with truncated multiplicities and moving targets, 2004 (Preprint math.CV/0405557)

[2] G. Dethloff; Tran Van Tan An extension of uniqueness theorems for meromorphic mappings, 2004 (Preprint math.CV/0405558)

[3] H. Fujimoto The uniqueness problem of meromorphic maps into the complex projective space, Nagoya Math. J., Volume 58 (1975), pp. 1-23 | MR | Zbl

[4] H. Fujimoto Uniqueness problem with truncated multiplicities in value distribution theory, Nagoya Math. J., Volume 152 (1998), pp. 131-152 | MR | Zbl

[5] H. Fujimoto Uniqueness problem with truncated multiplicities in value distribution theory, II, Nagoya Math. J., Volume 155 (1999), pp. 161-188 | MR | Zbl

[6] S. Ji Uniqueness problem without multiplicities in value distribution theory, Pacific J. Math., Volume 135 (1988), pp. 323-348 | MR | Zbl

[7] D. Q. Manh Unique range sets for holomorphic curves, Acta Math. Vietnam, Volume 27 (2002), pp. 343-348 | MR | Zbl

[8] R. Nevanlinna Einige Eindeutigkeitssätze in der Theorie der meromorphen Funktionen, Acta. Math., Volume 48 (1926), pp. 367-391

[9] M. Ru; W. Stoll The Second Main Theorem for moving targets, J. Geom. Anal., Volume 1 (1991), pp. 99-138 | MR | Zbl

[10] M. Ru A uniqueness theorem with moving targets without counting multiplicity, Proc. Amer. Math. Soc., Volume 129 (2002), pp. 2701-2707 | MR | Zbl

[11] L. Smiley Geometric conditions for unicity of holomorphic curves, Contemp. Math., Volume 25 (1983), pp. 149-154 | MR | Zbl

[12] Z.-H. Tu Uniqueness problem of meromorphic mappings in several complex variables for moving targets, Tohoku Math. J., Volume 54 (2002), pp. 567-579 | MR | Zbl

[13] W. Yao Two meromorphic functions sharing five small functions in the sense E ¯ (k) (β,f)=E ¯ (k) (β,g), Nagoya Math. J., Volume 167 (2002), pp. 35-54 | MR | Zbl

Cité par Sources :