Algebraic Criterion on Quasiconformal Equivalence of Riemann Surfaces

Abstract

1. Various strides have been done to characterize the conformal structure of Riemann surfaces by the algebraic structure of some appropriate function algebras on them (cf. Bers [2], Rudin [29], Royden [26], [28], Heins [7], Kakutani [12], Wermer [33] etc.). In this paper we discuss, corresponding to the above, the problem to determine the quasiconformal structure of Riemann surfaces by the algebraic structure of some function algebras on them.