The essential maximality and some other properties of a Riemann surface of \(O^ 0_{AD}\) (Q1068981)

It is well-known that a Riemann surface R of finite genus belonging to the null class \(O_{AD}\) is essentially maximal, and on the other hand, by Myrberg's example, there are Riemann surfaces of infinite genus belonging to \(O_{AD}\) which are not essentially maximal [cf. \textit{L. Sario} and \textit{M. Nakai}, Classification theory of Riemann surfaces (1970; Zbl 0199.406) for details]. The present author demonstrates that for any Riemann surface R belonging to the subclass \(O^ 0_{AD}\), R is essentially maximal. This very nice result is connected with a modified Stoïlow principle also proved in the paper.