Determination of the type and properties of the mapping function of a class of doubly-connected Riemann surfaces

Howard E. Taylor
1953 Proceedings of the American Mathematical Society  
lent to a semi-infinite cylinder, hence is open and simply-connected. Therefore J is either hyperbolic or parabolic. The nature of the singularities of J depends on the sequences {an\, {bn}-(1) If neither sequence has a limit, J has no singularities. (2) If one of the sequences has a limit or if both have the same limit,
doi:10.1090/s0002-9939-1953-0053252-5 fatcat:vmsoepzmxfh75l3fgskzlsxbwa