Uniqueness of meromorphic mappings partially shared hypersurfaces
Main Article Content
Abstract
The purpose of this paper is to study uniqueness problem of meromorphic mapping from Cm into the complex space Pn(C) sharing partial fixed and moving hypersurfaces. Using the second main theorems due to S. D. Quang and D. P. An [12, 13], we obtain some uniqueness results. Our results are improved some before results in this trend. In our best knowledge, there are not any uniqueness results of meromorphic mapping partially shared hypersurfaces up to now.
Article Details
Keywords
Hypersurfaces, Meromorphic mapping, Nevanlinna theory, Uniqueness theorem
References
[1] Cao, T. B, Yi, H. X, On the multiple values and uniqueness of meromorphic functions sharing small functions as targets, Bull. Korean Math. Soc, 44(4) (2007), 631-640.
[2] Cartan, H., Sur les zeros des combinaisions linearires de p fonctions holomorpes donnees, Mathematica (Cluj), 7 (1933), 80-103.
[3] Chen, T. G, Chen, K. Y, Tsai, Y. L, Some generalizations of Nevanlinna’s five value theorem, Kodai Math. J, 30(3) (2007), 438-444.
[4] Chen, Y., Yan, Q., A note on uniqueness problem for meromorphic mappings with 2N + 3 hyperplanes, Sci. China Math, 53(10) (2010), 2657-2663.
[5] Dethloff, G., Tan, T. V, A Uniqueness Theorem for Meromorphic Maps with Moving Hypersurfaces, Publ. Math. Debrecen, 78 (2011), 347-357.
[6] Dulock, M., Ru, M., A uniqueness theorem for holomorphic curves into encountering hypersurfaces in projective space, Complex Variables and Elliptic Equations, 53 (2008), 797-802.
[7] Lahiri, I., Pal, R., A note on Nevanlinna’s Five Value Theorem, Bull. Korean Math. Soc, 52(2) (2015), 345-350.
[8] Fujimoto, H., The uniqueness problem of meromorphic maps into complex projective spaces, Nagoya Math. J, 58 (1975), 1-23.
[9] Gopalakrishna, H. S, Bhoosnurmath, S. S, Uniqueness theorems for meromorphic functions, Math. Scand, 39(1) (1976), 125-130.
[10] Hu, P. C, Li, P., Yang, C. C, Unicity of meromorphic mappings, Kluwer, 2003.
[11] Phuong, H. T, On unique range sets for holomorphic maps sharing hypersurfaces without counting multiplicity, Acta. Math. Vietnamica, 34(3) (2009), 351-360.
[12] Quang, S. D, An, D. P, Second Main Theorem and unicity of meromorphic mappings for hypersurfaces in projective varieties, Acta Mathematica Vietnamica, 42(3) (2017), 455-470.
[13] Quang, S. D, An, D. P, Second Main Theorems for meromorphic mappings with moving hypersurfaces and a uniqueness problem, Computational Methods and Function Theory, 17(3) (2017), 445-461.
[14] Ru, M., A defect relation for holomorphic curves intersecting hypersurfaces, Amer. Journal of Math, 126 (2004), 215-226.
[15] Smiley, L., Geometry conditions for unicity of holomorphic curves, Contemp. Math, 25 (1983), 149-154.
[2] Cartan, H., Sur les zeros des combinaisions linearires de p fonctions holomorpes donnees, Mathematica (Cluj), 7 (1933), 80-103.
[3] Chen, T. G, Chen, K. Y, Tsai, Y. L, Some generalizations of Nevanlinna’s five value theorem, Kodai Math. J, 30(3) (2007), 438-444.
[4] Chen, Y., Yan, Q., A note on uniqueness problem for meromorphic mappings with 2N + 3 hyperplanes, Sci. China Math, 53(10) (2010), 2657-2663.
[5] Dethloff, G., Tan, T. V, A Uniqueness Theorem for Meromorphic Maps with Moving Hypersurfaces, Publ. Math. Debrecen, 78 (2011), 347-357.
[6] Dulock, M., Ru, M., A uniqueness theorem for holomorphic curves into encountering hypersurfaces in projective space, Complex Variables and Elliptic Equations, 53 (2008), 797-802.
[7] Lahiri, I., Pal, R., A note on Nevanlinna’s Five Value Theorem, Bull. Korean Math. Soc, 52(2) (2015), 345-350.
[8] Fujimoto, H., The uniqueness problem of meromorphic maps into complex projective spaces, Nagoya Math. J, 58 (1975), 1-23.
[9] Gopalakrishna, H. S, Bhoosnurmath, S. S, Uniqueness theorems for meromorphic functions, Math. Scand, 39(1) (1976), 125-130.
[10] Hu, P. C, Li, P., Yang, C. C, Unicity of meromorphic mappings, Kluwer, 2003.
[11] Phuong, H. T, On unique range sets for holomorphic maps sharing hypersurfaces without counting multiplicity, Acta. Math. Vietnamica, 34(3) (2009), 351-360.
[12] Quang, S. D, An, D. P, Second Main Theorem and unicity of meromorphic mappings for hypersurfaces in projective varieties, Acta Mathematica Vietnamica, 42(3) (2017), 455-470.
[13] Quang, S. D, An, D. P, Second Main Theorems for meromorphic mappings with moving hypersurfaces and a uniqueness problem, Computational Methods and Function Theory, 17(3) (2017), 445-461.
[14] Ru, M., A defect relation for holomorphic curves intersecting hypersurfaces, Amer. Journal of Math, 126 (2004), 215-226.
[15] Smiley, L., Geometry conditions for unicity of holomorphic curves, Contemp. Math, 25 (1983), 149-154.