Asymptotics of Conformal Module of Nonsymmetric Doubly Connected Domain under Unbounded Stretching Along the Real Axis

Abstract

We establish an asymptotic formula describing the behavior of the conformal module of a plane doubly connected domain under its stretching along the real axis with coefficient tending to infinity. The description is given in simple geometric terms, connected with equations of the boundary curves. Therefore, in the nonsymmetric case we give an answer to a problem by Prof. M. Vourinen.