Tohoku Mathematical Journal
2002
December
SECOND SERIES VOL. 54, NO. 4

Tohoku Math. J.
54 (2002), 567-579

Title UNIQUENESS PROBLEM OF MEROMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES FOR MOVING TARGETS

Author Zhen-Han Tu

(Received September 13, 2000, revised April 9, 2001)
Abstract. Nevanlinna showed that for two nonconstant meromorphic functions on the complex plane, if they have the same inverse images counting multiplicities for four distinct values, then they coincide up to a Möbius transformation, and if they have the same inverse images for five distinct values, then they coincide. Fujimoto and Smiley extended Nevanlinna's uniqueness theorems to the case of meromorphic mappings of several complex variables into the complex projective space for hyperplanes. Recently, Motivated by Ru Min and Stoll's accomplishment of the second main theorem for moving targets, Li Baoqin and Shirosaki proved some uniqueness theorems of entire functions in several complex variables and meromorphic functions in one complex variable, respectively, for moving targets. Using the techniques of value distribution theory in several complex variables, we prove some uniqueness theorems of meromorphic mappings of several complex variables into the complex projective space for moving targets.

2000 Mathematics Subject Classification. Primary 32H30; Secondary 30D35.
Key words and phrases. Complex projective spaces, meromorphic mappings, uniqueness theorems and value distribution theory.

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