Nevanlinna showed that two distinct non-constant meromorphic functions on C must be linked by a Mo ¨bius transformation if they have the same inverse images counted with multiplicities for four distinct values. Later on, Gundersen generalized the result of Nevanlinna to the case where two meromorphic functions share two values ignoring multiplicity and share other two values with counting multiplicities. In this paper, we will extend the results of Nevanlinna-Gundersen to the case of two holomorphic mappings into P n ðCÞ sharing ðn þ 1Þ hyperplanes ignoring multiplicity and other ðn þ 1Þ hyperplanes with multiplicities counted to level 2 or ðn þ 1Þ.
Abstract. Nevanlinna showed that two non-constant meromorphic functions on C must be linked by a Möbius transformation if they have the same inverse images counted with multiplicities for four distinct values. After that this results is generalized by Gundersen to the case where two meromorphic functions share two values ignoring multiplicity and share other two values with multiplicities trucated by 2. Previously, the first author proved that for n ≥ 2, there are at most two linearly nondegenerate meromorphic mappings of C m into P n (C) sharing 2n + 2 hyperplanes ingeneral position ignoring multiplicity. In this article, we will show that if two meromorphic mappings f and g of C m into P n (C) share 2n + 1 hyperplanes ignoring multiplicity and another hyperplane with multiplicities trucated by n + 1 then the map f × g is algebraically degenerate.
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