On the order of holomorphic curves with maximal deficiency sum (Q1911165)

Let \(f\) be a transcendental meromorphic function of finite order in the complex plane. For a complex value \(a\), \(\delta(a,f)\) denotes the deficiency of \(a\) with respect to \(f\). \textit{A. Edrei} and \textit{W. H. J. Fuchs} [Trans. Am. Math. Soc. 93, 292-328 (1959; Zbl 0092.07201)] proved that if \(\delta(\infty, f) = 1\) and \(\sum_{a \neq \infty} \delta(a, f) = 1\), then \(f\) is of regular growth and the order of \(f\) is a positive integer. This is a special case of a conjecture of F. Nevanlinna which has been completely solved by \textit{D. Drasin} [Acta. Math. 158, 1-94 (1987; Zbl 0622.30028)]. In the paper under review, the author gives a generalisation of the result of Edrei and Fuchs to holomorphic curves \(f: C \to P^n(C)\). The case of moving targets (i.e. functions \(a\) growing small with respect to \(f\)) is considered also.