Bloch’s principle and normal criterion. (English) Zbl 0687.30023

Pang, Xuecheng

Sci. China, Ser. A 32, No. 7, 782-791 (1989).

L. Zalcman [Am. Math. Monthly 82, 813-817 (1975; Zbl 0315.30036)] gave a precise form of the heuristic principle that “a family of holomorphic functions which have a common property \(P\) in a domain \(D\) is (apt to be) a normal family in \(D\) if \(P\) cannot be possessed by a non-constant entire function in the finite plane”. The author uses a modified version of Zalcman’s principle to establish the normality of the family \(F\) of meromorphic functions \(f(z)\) satisfying \(f^ nf'\neq 1\) (\(n\geq 2\)) in a domain \(D\).

Reviewer: St.Dragosh

MSC:

30D45

Normal functions of one complex variable, normal families

Keywords:

Bloch’s principle; normal family

Citations:

Zbl 0315.30036