Asymptotics of the conformal modulus of a nonsymmetric unbounded doubly-connected domain under stretching

Abstract

We describe the asymptotic behavior of the conformal modulus of an unbounded doubly-connected domain, non-symmetric with respect to the coordinate axes, when stretched in the direction of the abscissa axis with coefficient $H\to +\infty$. Therefore, we give a partial answer to a problem, suggested by M.~Vourinen, for the case of an arbitrary unbounded domain.