Previous |  Up |  Next

Article

Title: Weak normal and quasinormal families of holomorphic curves (English)
Author: Quang, Si Duc
Author: Quan, Dau Hong
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 54
Issue: 3
Year: 2018
Pages: 153-163
Summary lang: English
.
Category: math
.
Summary: In this paper we introduce the notion of weak normal and quasinormal families of holomorphic curves from a domain in $\mathbb{C}$ into projective spaces. We will prove some criteria for the weak normality and quasinormality of at most a certain order for such families of holomorphic curves. (English)
Keyword: weak normal
Keyword: quasinormal family
Keyword: holomorphic curve
Keyword: meromorphic mappings
MSC: 30D35
MSC: 32H02
MSC: 32H04
MSC: 32H30
idZBL: Zbl 06940795
idMR: MR3847322
DOI: 10.5817/AM2018-3-153
.
Date available: 2018-08-07T13:35:11Z
Last updated: 2020-01-05
Stable URL: http://hdl.handle.net/10338.dmlcz/147350
.
Reference: [1] Aladro, G., Krantz, S.G.: A criterion for normality in $\mathbb{C}^n$.J. Math. Anal. Appl. 161 (1991), 1–8. MR 1127544, 10.1016/0022-247X(91)90356-5
Reference: [2] Bar, R., Grahl, J., Nevo, S.: Differential inequalities and quasinormal families.Anal. Math. Phys. 4 (2004), 66–71. MR 3215192
Reference: [3] Chuang, C.T.: Normal families of meromorphic functions.World Scientific Publishing Co. Pte. Ltd., 1993. MR 1249270
Reference: [4] Dethloff, G., Thai, D.D., Trang, P.N.T.: Normal families of meromorphic mappings of several complex variables for moving hypersurfaces in a complex projective space.Nagoya Math. J. 217 (2015), 23–59. MR 3343838, 10.1215/00277630-2863882
Reference: [5] Fujimoto, H.: On families of meromorphic maps into the complex projective space.Nagoya Math. J. 54 (1974), 21–51. MR 0367301, 10.1017/S0027763000024570
Reference: [6] Mai, P.N., Thai, D.D., Trang, P.N.T.: Normal families of meromorphic mappings of several complex variables into $¶^N(\mathbb{C})$.Nagoya Math. J. 180 (2005), 91–110. MR 2186670, 10.1017/S002776300000920X
Reference: [7] Nevo, S., Pang, X., Zalcman, L.: Quasinormality and meromorphic functions with multiple zeros.J. d'Analyse Math. 101 (2007), 1–23. MR 2346538, 10.1007/s11854-007-0001-5
Reference: [8] Noguchi, J., Ochiai, T.: Introduction to geometric function theory in several complex variables.Transl. Math. Monogr. (1990). MR 1084378, 10.1090/mmono/080
Reference: [9] Noguchi, J., Winkelmann, J.: Holomorphic curves and integral points off divisors.Math. Z. 239 (2002), 593–610. MR 1893854, 10.1007/s002090100327
Reference: [10] Pang, X., Nevo, S., Zalcman, L.: Quasinormal families of meromorphic functions.Rev. Mat. Iberoamericana 21 (2005), 249–262. MR 2155021, 10.4171/RMI/422
Reference: [11] Quang, S.D.: Extension and normality of meromorphic mappings into complex projective varieties.Ann. Polon. Math. 104 (2012), 279–292. MR 2914536, 10.4064/ap104-3-5
Reference: [12] Quang, S.D., Tan, T.V.: Normal families of meromorphic mappings of several complex variables into $\mathbb{C}P^n$ for moving hypersurfaces.Ann. Polon. Math. 94 (2008), 97–110. MR 2438852, 10.4064/ap94-2-1
Reference: [13] Stoll, W.: Normal families of non-negative divisors.Math. Z. 84 (1964), 154–218. MR 0165142, 10.1007/BF01117123
Reference: [14] Thai, D.D., Trang, P.N.T., Huong, P.D.: Families of normal maps in several complex variables and hyperbolicity of complex spaces.Complex Var. Elliptic Equ. 48 (2003), 469–482. MR 1979525
Reference: [15] Zalcman, L.: Normal families, new perspectives.Bull. Amer. Math. Soc. 35 (1998), 215–230. MR 1624862, 10.1090/S0273-0979-98-00755-1
.

Files

Files Size Format View
ArchMathRetro_054-2018-3_3.pdf 524.0Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo