On the non-existence of unbounded domains of normality of meromorphic functions (Q5957163)

\textit{I. N. Baker} [J. Aust. Math. Soc., Ser. A 30, 483-495 (1981; Zbl 0474.30023)] discussed the non-existence of unbounded components of the Fatou set of a transcendental entire function \(f\) of small growth, raised the question of whether every component of the Fatou set \(F(f)\) of \(f\) must be bounded if \(f\) is of sufficiently small growth, and proved that every invariant component of \(F(f)\) is bounded if \(f\) is of order \(<1/2\), and of minimal type. The main result of the author is the following: If \(f\) is a transcendental meromorphic function in \(\mathbb{C}\) satisfying NEWLINE\[NEWLINE\limsup_{r\to\infty}\frac{m(r,f)}{r}=\infty,NEWLINE\]NEWLINE where NEWLINE\[NEWLINEm(r,f)=\min\{|f(z)|\mid |z|=r\},NEWLINE\]NEWLINE then the Fatou set \(F(f)\) of \(f\) has no unbounded preperiodic or periodic components.