Some unsolved problems on meromorphic functions of uniformly bounded characteristic

摘要

The familyUBC(R)of meromorphic functions of uniformly bounded characteristic in a Rieman surfaceRis defined in terms of the Shimizu-Ahlfors characteristic function. There are some natural parallels betweenUBC(R)andBMOA(R), the family of holomorphic functions of bounded mean oscillation inR. After a survey some open problems are proposed in contrast withBMOA(R).