Two meromorphic mappings sharing 2n+2 hyperplanes regardless of multiplicity

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 result is generalized by Gundersen to the case where two meromorphic functions share two values ignoring multiplicity and share other two values with multiplicities truncated by 2. Previously, the first author proved that for n⩾2, there are at most two linearly non-degenerate meromorphic mappings of Cm into Pn(C) sharing 2n+2 hyperplanes ingeneral position ignoring multiplicity. In this article, we will show that if two meromorphic mappings f and g of Cm into Pn(C) share 2n+1 hyperplanes ignoring multiplicity and another hyperplane with multiplicities truncated by n+1 then the map f×g is algebraically degenerate.