A unicity theorem for moving targets counting multiplicities

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 Möbius 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.