“…As it will be shown, Theorem i', in turn, follows from a combination of the result for the case when ~ is the unit circumference and some properties of conformal mappings, established in [3] and [4]. We note that from the proof of Theorem 2 it will follow that for ~-~0 the estimate (6) is unimprovable with respect to the order, i.e., for each g, 0<e-<~, there exists a curve hg with a homomorphism ~ such that…”