Moebius Transformations, the Caratheodory Metric, and the Objects of Complex Analysis and Potential Theory in Multiply Connected Domains

摘要

Let f_b denote the Riemann mapping function associated to a point b in a simply connected planar domain Ω = C. Everyone knows that f_b, is the solution to an extremal problem; it is the holomorphic map h of Ω into the unit disc such that h'(b) is real and as large as possible.