Value distribution of holomorphic mappings of \({\mathbb{C}}^ m\) into a Banach space (Q1097378)

The celebrated theorem of Ahlfors concerning value distribution of meromorphic functions is generalized to holomorphic maps from \({\mathbb{C}}^ m\) to an arbitrary Banach space X. The method of proof used in the paper relies on a concept of plurisubharmonic functions defined in \(X^*\), which is different from that developed by \textit{P. Lelong} [Lect. Notes Math. 71, 167-190 (1968; Zbl 0165.450)] and \textit{C. O. Kiselman} [Ann. Inst. Fourier 34, 155-183 (1984; Zbl 0523.32012)]. This also allows the author to simplify proofs of known results generalizing Ahlfors' theorem to holomorphic mappings of complex manifolds into compact complex manifolds.