Geodesic
Teikhmyuller problem for one class of open Riemannian surfaces
Matematičeskie zametki, Tome 7 (1970) no. 5, pp. 605-615.

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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. 
@article{MZM_1970_7_5_a8,
     author = {V. V. Dumkin and V. G. Sheretov},
     title = {Teikhmyuller problem for one class of open {Riemannian} surfaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {605--615},
     publisher = {mathdoc},
     volume = {7},
     number = {5},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_7_5_a8/}
}
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V. V. Dumkin; V. G. Sheretov. Teikhmyuller problem for one class of open Riemannian surfaces. Matematičeskie zametki, Tome 7 (1970) no. 5, pp. 605-615. http://geodesic.mathdoc.fr/item/MZM_1970_7_5_a8/