A Generalization of Lappan's Theorem to Higher Dimensional Complex Projective Space

In this paper,the authors discuss a generalization of Lappan’s theorem to higher dimensional complex projective space and get the following result:Let f be a holomorphic mapping of△into P^(n)(C),and let H_(1),…,H_(q)be hyperplanes in general position in P^(n)(C).Assume that sup{(1-|z|^(2))f^(#)(z):z∈q∪j=1f^(-1)(H_(j))}<∞,if q≥2n^(2)+3,then f is normal.