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Uniqueness Problem for Meromorphic Mappings with Truncated Multiplicities and Moving Targets

Published online by Cambridge University Press:  11 January 2016

Gerd Dethloff
Affiliation:
Universitée de Bretagne Occidentale, UFR Sciences et Techniques, Département de Mathématiques, 6, avenue Le Gorgeu, BP 452 29275 Brest Cedex, [email protected]
Tran Van Tan
Affiliation:
Universitée de Bretagne Occidentale, UFR Sciences et Techniques, Département de Mathématiques, 6, avenue Le Gorgeu, BP 452 29275 Brest Cedex, France
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Abstract

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In this paper, using techniques of value distribution theory, we give a uniqueness theorem for meromorphic mappings of ℙm into ℙPn with (3n+1) moving targets and truncated multiplicities.

Keywords

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2006

References

[1] Fujimoto, H., The uniqueness problem of meromorphic maps into the complex projective space, Nagoya Math. J., 58 (1975), 123.CrossRefGoogle Scholar
[2] Fujimoto, H., Uniqueness problem with truncated multiplicities in value distribution theory, Nagoya Math. J., 152 (1998), 131152.CrossRefGoogle Scholar
[3] Fujimoto, H., Uniqueness problem with truncated multiplicities in value distribution theory, II, Nagoya Math. J., 155 (1999), 161188.CrossRefGoogle Scholar
[4] Gundersen, G., Meromorphic functions that share four values, Trans. Amer. Math. Soc., 277 (1983), 545567.Google Scholar
[5] Ji, S., Uniqueness problem without multiplicities in value distribution theory, Pacific J. Math., 135 (1988), 323348.CrossRefGoogle Scholar
[6] Nevanlinna, R., Einige Eideutigkeitssätze in der Theorie der meromorphen Funktionen, Acta. Math., 48 (1926), 367391.CrossRefGoogle Scholar
[7] Noguchi, J. and Ochiai, T., Geometric function theory in several complex variables, Trans. Math. Monogr. 80, Amer. Math. Soc, Providence, Rhode Island, 1990.Google Scholar
[8] Ru, M. and Stoll, W., The Second Main Theorem for moving targets, J. Geom. Anal., 1 (1991), 99138.Google Scholar
[9] Ru, M., A uniqueness theorem with moving targets without counting multiplicity, Proc. Amer. Math. Soc, 129 (2001), 27012707.Google Scholar
[10] Smiley, L., Geometric conditions for unicity of holomorphic curves, Contemp. Math., 25 (1983), 149154.CrossRefGoogle Scholar
[11] Tu, Z.-H., Uniqueness problem of meromorphic mappings in several complex variables for moving targets, Tohoku Math. J., 54 (2002), 567579.CrossRefGoogle Scholar
[12] Yao, W., Two meromorphic functions sharing five small functions in the sense Ēk) (β, f) = Ēk) (β,g), Nagoya Math. J., 167 (2002), 3554.Google Scholar
[13] Dethloff, G. and Tan, Tran Van, An extension of uniqueness theorems for meromorphic mappings, to appear in Vietnam Journal of Mathematics (2006).Google Scholar