Degeneracy and finiteness theorems for meromorphic mappings in several complex variables

In this article, we prove that there are at most two meromorphic mappings of ${\mathbb{C}}^m$ into ${\mathbb{P}}^n(\mathbb{C})(n⩾2)$ sharing $2n+2$ hyperplanes in general position regardless of multiplicity, where all zeros with multiplicities more than certain values do not need to be counted. We also show that if three meromorphic mappings $f^1,f^2,f^3$ of ${\mathbb{C}}^m$ into ${\mathbb{P}}^n(\mathbb{C})(n⩾5)$ share $2n+1$ hyperplanes in general position with truncated multiplicity then the map $f^1\times f^2\times f^3$ is linearly degenerate.