The Discontinuity Function of Discrete Groups and Radius of Schlichtness

摘要

We define the notion of the discontinuity radius of a discrete and discontinuous group. This is a function which is closely related to the group geometry. We demonstrate the usefullness of this notion by proving some geometrical results and by computing the schlichtness radius of certain Blaschke products. In a subsequent paper we will give further applications to Fuchsian groups.