UNIQUE DETERMINATION OF 3-CONNECTED PLANE DOMAINS BY RELATIVE CONFORMAL MODULI OF PAIRS OF BOUNDARY COMPONENTS

摘要

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 conformal moduli (extremal lengths) of pairs of boundary components of a domain of connectedness at most 3. Bibliography: 12 titles.