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

Abstract

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 Δ into ℙⁿ(ℂ), and let H₁, ⋯, H_q be hyperplanes in general position in ℙⁿ(ℂ). Assume that

$$\sup \left\{ {\left( {1 - {{\left| z \right|}^2}} \right){f^\sharp }\left( z \right):z \in \bigcup\limits_{j = 1}^q {{f^{ - 1}}\left( {{H_j}} \right)} } \right\} < \infty ,$$

if q ≥ 2n² + 3, then f is normal.