On the Margulis constant for Kleinian groups. I.
We give a bound for the number of coincidence of two morphisms between given compact Riemann surfaces (complete complex algebraic curves). Our results generalize well known facts about the number of fixed points of an automorphism.
We obtain short and unified new proofs of two recent characterizations of hyperellipticity given by Maskit (2000) and Schaller (2000), as well as a way of establishing a relation between them.