Some unsolved problems on meromorphic functions of uniformly bounded characteristic (Q1076194)

The author continues his study of meromorphic functions of uniformly bounded characteristic on a domain. In this paper the family of meromorphic functions of uniformly bounded characteristic on a Riemann surface R is defined using the Ahlfors-Shimizu characteristic function. The author notes parallels between this family and the family of holomorphic functions of bounded mean oscillation in R defined by Tom Metzger; the latter is a subset of the set of all holomorphic functions of uniformly bounded characteristic on R. Following a short listing of properties of these families, there is a list of seven open problems about them.