Tohoku Mathematical Journal
2005
December
SECOND SERIES VOL. 57, NO. 4

Tohoku Math. J.
57 (2005), 589-595

Title A UNICITY THEOREM FOR MOVING TARGETS COUNTING MULTIPLICITIES

Author Lu Jin and Min Ru

(Received December 8, 2003, revised July 27, 2004)
Abstract. R. Nevanlinna showed, in 1926, that for two nonconstant meromorphic functions on the complex plane, if they have the same inverse images counting multiplicities for four distinct complex values, then they coincide up to a Mobius transformation, and if they have the same inverse images counting multiplicities for five distinct complex values, then they are identical. H. Fujimoto, in 1975, extended Nevanlinna's result to nondegenerate holomorphic curves. This paper extends Fujimoto's uniqueness theorem to the case of moving hyperplanes in pointwise general position.

2000 Mathematics Subject Classification. Primary 32H30; Secondary 32H25.
Key words and phrases. Holomorphic maps, unicity theorem, moving targets.

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