Some results on the uniqueness of meromorphic mappings (Q1044826)

Let \(f, g\) be linearly non-degenerate meromorphic mappings from \(\mathbb C^m\) to \(\mathbb C\mathbb P^n\) and \(\{H_j\}_{j=1}^q\) \(q\) hyperplanes in general position in \(\mathbb C\mathbb P^n\) with \(\dim(f^{-1}(H_i)\cap f^{-1}(H_j))\leq m-2\) for all \(1\leq i < j \leq q\). Let \(\overline{E}(H, f)\) be the zero set of \((f, H)\). In this paper, the authors extend some uniqueness theorems from meromorphic functions to meromorphic mappings. For instance, the authors prove that \(f\equiv g\) if \(\overline{E}(H_j, f) \subset \overline{E}(H_j, g)\), \(f=g\) on \(\bigcup_{j=1}^qf^{-1}(H_j)\), \(q=3n+2\) and \(\liminf_{r \to \infty}(\sum_1^qN^1_{(f, H_j)}(r))/(\sum_1^qN^1_{(g, H_j)}(r))>n/(n+1)\).