Abstract
In this paper, we extend the concept of holomorphic curves sharing hyperplanes and introduce definitions of restricted hyperplanes and partial shared hypersurfaces. Then, we prove several normal criteria of the family of holomorphic curves and holomorphic mappings that concern restricted hyperplanes and partial shared hypersurfaces. These results generalize the Montel-type normal criterion of holomorphic curves.
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References
Aladro G, Krantz S G. A criterion for normality in ℂn. J Math Anal Appl, 1991, 161: 1–8
Bergweiler W. Bloch’s principle. Comput Methods Funct Theory, 2006, 6(1): 77–108
Chai F J, Gao Z S. The normality of algebroid multifunctions and their coefficient functions. Acta Math Sci, 2015, 35B(1): 121–132
Fujimoto H. On families of meromorphic maps into the complex projective space. Nagoya Math J, 1974, 54: 21–51
Hayman W K. Meromorphic Functions. Oxford: Clarendon Press, 1964
Liu X Y. Normal families and shared values of meromorphic functions. Bull Malays Math Sci Soc, 2016, 39: 155–171
Liu X J, Li L S, Pang X C. A normal criterion about two families of meromorphic functions concerning shared values. Acta Math Sin-Engl Series, 2013, 29(1): 151–158
Ru M. Nevanlinna Theory and its Relation to Diophantine Approximation. Singapore: World Scientific, 2001
Sun D C. Normality criteria for families of meromorphic algebroid functions. Acta Math Sci, 2010, 30B(1): 166–172
Sun D C, Yang L. Normal families of algebroidal functions. Sci China Ser A, 2001, 44: 1271–1277
Sun D C, Liu H F. Normal criteria on the family of meromorphic functions with shared set. Isr J Math, 2011, 184: 403–412
Shabat B V. Distribution of Values of Holomorphic Mappings. Translations of Mathematical Monographs 61. Providence, RI: Amer Math Soc, 1985
Tu Z H. Normality criteria for families of holomorphic mappings of several complex variables into ℙn(ℂ). Proc Amer Math Soc, 1999, 127(4): 1039–1049
Wu H. Normal families of holomorphic mappings. Acta Math, 1967, 119: 193–233
Yang L, Fang C Y, Pang X C. Normal families of holomorphic mappings into complex projective space concerning shared hyperplanes. Pac J Math, 2014, 272(1): 245–256
Yang L, Liu X J, Pang X C. On families of meromorphic map into the complex projective space. Housten J Math, 2016, 42(3): 775–789
Zalcman L. Normal families: new perspectives. Bull Amer Math Soc, 1998, 35: 215–230
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Dedicated to the memory of Professor Jiarong YU
The second author was supported by the National Natural Science Foundation of China (11501127), Foundation for Distinguished Young Talents in Higher Education of Guangdong Province (2014KQNCX068). The third author was supported by the Foundation of Guangzhou Civil Aviation College (18X0428).
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Sun, D., Huo, Y. & Chai, F. Normal Criteria for a Family of Holomorphic Curves. Acta Math Sci 41, 1887–1895 (2021). https://doi.org/10.1007/s10473-021-0606-2
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DOI: https://doi.org/10.1007/s10473-021-0606-2
Key words
- complex projective spaces
- holomorphic curves
- holomorphic mappings
- normal families
- restricted hyperplanes