Abstract:
We study the boundary values of conformal mappings of plane finitely-connected domains. We present a 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 $3$.
Keywords:finitely-connected plane domain, relative conformal modulus of a pair of boundary components of the domain, Teichmüller and Grötzsch extremal domains.