Uniqueness theorem for holomorphic mappings on annuli sharing few hyperplanes

  • Ha Huong Giang Electric Power Univ., Hanoi, Vietnam

Abstract

UDC 517.5

We prove a uniqueness theorem of linearly nondegenerate holomorphic mappings from annulus to complex projective space $\mathbb{P}^n(\mathbb{C} )$ with different multiple values and a general condition on the intersections of the inverse images of these hyperplanes.

References

T. B. Cao, Z. S. Deng, On the uniqueness of meromorphic functions that share three or two finite sets on annuli, Proc. Indian Acad. Sci., 122, No 2, 203 – 220 (2012), https://doi.org/10.1007/s12044-012-0074-7 DOI: https://doi.org/10.1007/s12044-012-0074-7

Z. Chen, Q. Yan, Uniqueness theorem of meromorphic mappings into $Bbb P^N(Bbb C)$ sharing $2N+3$ hyperplanes regardless of multiplicities, Internat. J. Math., 20, 717 – 726 (2009), https://doi.org/10.1142/S0129167X09005492 DOI: https://doi.org/10.1142/S0129167X09005492

H. Fujimoto, The uniqueness problem of meromorphic maps into the complex projective space, Nagoya Math. J., 58, 1 – 23 (1975). DOI: https://doi.org/10.1017/S0027763000016676

H. H. Giang, L. N. Quynh, S. D. Quang, Uniqueness theorems for meromorphic mappings sharing few hyperplanes, J. Math. Anal. and Appl., 393, 445 – 456 (2012), https://doi.org/10.1016/j.jmaa.2012.03.049 DOI: https://doi.org/10.1016/j.jmaa.2012.03.049

A. Y. Khrystiyanyn, A. A. Kondratyuk, On the Nevanlinna theory for meromorphic functions on annuli, I, Mat. Stud., 23, № 01, 19 – 30 (2005).

A. Y. Khrystiyanyn, A. A. Kondratyuk, On the Nevanlinna theory for meromorphic functions on annuli, II, Mat. Stud., 24, № 02, 57 – 68 (2005).

M. Lund, Z. Ye, Nevanlinna theory of meromorphic functions on annuli, Sci. China Math., 53, 547 – 554 (2010), https://doi.org/10.1007/s11425-010-0037-3 DOI: https://doi.org/10.1007/s11425-010-0037-3

R. Nevanlinna, Einige Eindeutigkeitssate in der Theorie der meromorphen Funktionen, Acta Math., 48, 367 – 391 (1926), https://doi.org/10.1007/BF02565342 DOI: https://doi.org/10.1007/BF02565342

L. Smiley, Geometric conditions for unicity of holomorphic curves, Contemp. Math., 25, 149 – 154 (1983), https://doi.org/10.1090/conm/025/730045 DOI: https://doi.org/10.1090/conm/025/730045

Published
22.02.2021
How to Cite
Giang, H. H. “Uniqueness Theorem for Holomorphic Mappings on Annuli Sharing Few Hyperplanes”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 2, Feb. 2021, pp. 249 -60, doi:10.37863/umzh.v73i2.107.
Section
Research articles