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Shared Hyperplanes and Normal Families of Holomorphic Curves
College of Science, University of Shanghai for Science and Technology, Shanghai, China
- 1 College of Science, University of Shanghai for Science and Technology, Shanghai, China
American Journal of Computational Mathematics·Volume 11 (2021)·Pages 83–93·Published 10 May 2021·DOI10.4236/ajcm.2021.112008
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Abstract
In theorem LP [1], Liu proves the theorem when N = 2, but it can’t be ex-tended to the general case in his proof. So we consider the condition that the families of holomorphic curves share eleven hyperplanes, and we get the theorem 1.1.
KeywordsHyperplaneNormal FamilyHolomorphic CurveHyperplanes of Share
- Liu, X.J. and Pang, X.C. (2020) Shared Hyperplanes and Normal Families of Holomorphic Curves. International Journal of Mathematics, 31, Article ID: 2050037. https://doi.org/10.1142/S0129167X20500378
- Zalcman, L. (1975) A Heuritic Principle in Complex Function Theory. The American Mathematical Monthly, 82, 813-817. https://doi.org/10.1080/00029890.1975.11993942
- Zalcman, L. (1998) Normal Families: New Perspectives. Bulletin of the American Mathematical Society, 35, 215-230. https://doi.org/10.1090/S0273-0979-98-00755-1
- Chen, Z.H. and Yan, Q.M. (2009) Uniqueness Theorem of Meromorphic Mappings into P N (C) Sharing 2N+3 Hyperplanes Regardless of Multiplicities. International Journal of Mathematics, 20, 717-726. https://doi.org/10.1142/S0129167X09005492
- Yang, L., Fang, C.Y. and Pang, X.C. (2014) Normal Families of Holomorphic Mappings into Complex Projective Space Concerning Shared Hyperplanes. Pacific Journal of Mathematics, 272, 245-256. https://doi.org/10.2140/pjm.2014.272.245
- Liu, X.J., Pang, X.C. and Yang, J.H. (2017) A Criterion of Normality Concerning Shared Hyperplanes. Chin. Chinese Annals of Mathematics, Series B, 38, 1-6.
- Ye, Y.S. Yang, L. and Pang, X.C. (2015) An Extension of Schwick’s Theorem for Normal Families. Annales Polonici Mathematici, 115, 23-31. https://doi.org/10.4064/ap115-1-2
- Aladroand, G. and Krantz, S.G. (1991) A Criterion for Normality in C n . Journal of Mathematical Analysis and Applications, 161, 1-8. https://doi.org/10.1016/0022-247X(91)90356-5
- Ru, M. (2001) Nevanlinna Theory and Its Relation to Diophantine Approximation. World Scientific, Singapore. https://doi.org/10.1142/4508
- Yang, L. (1993) Value Distribution Theory. Springer-Verlag, Berlin.