Unifying the little Picard, Lohwater–Pommerenke and Brody theorems

Abstract

A theorem unifying the theorems of little Picard, Lohwater-Pommerenke and Brody is presented: Let M, Y be complex spaces. Then a family of holomorphic maps F ⊂ H(M, Y ) is uniformly normal iff every F -limiting curve is trivial. Furthermore, Zalcman's lemma and the Robinson-Zalcman Heuristic Principle are 'extended.'