Higher dimensional generalizations of some classical theorems on normal meromorphic functions

Abstract

Generalizing the notion of normality of a meromorphic function to a holomorphic mapping of the unit ball Bm⊂C m into the complex projective space CPN, the author obtains several necessary and sufficient conditions for a holomorphic mapping f: Bm→CPN to be normal, thus generalizing the classical theorems of Lehto-Virtanen, Lohwater-Pommerenke and Lappan. It is also illustrated that the full generalizations of the theorems of Lohwater-Pommerenke and Lappan to a higher-dimensional domain are not likely to be true.