Teikhmyuller problem for one class of open Riemannian surfaces

A particular solution is given to the Teikhmyuller problem on minimizing the deviation $K[f]$ in the homotopic class $\alpha$, preserving the orientation of the quasiconformal homeomorphism $h: S_0\to S$, where $S_0$ and $S$ are open Riemannian surfaces of infinite kind. Some properties of the complex characteristic of the solution are studied.