On the Unique Determination of Three-Connected Plane Domain by the Relative Conformal Moduli of the Boundary Components
We study the boundary values of conformal mappings of plane ﬁnitely-connected domains. We presenta complete exposition of a theorem giving an exhaustive description of the boundary values of such mappings in terms of the conformal moduli(extremal lengths) of the pairs of boundary components of the domain under consideration in the case where its connectedness is at most 3.