Geodesic
Some extremal properties of conformal mappings of a~multiply connected domain onto canonical $p$-sheeted surfaces
Matematičeskie zametki, Tome 23 (1978) no. 2, pp. 261-270.

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Some theorems of Kühnau on the mutual position of the boundary components of images of a multiply connected domain under single-sheeted conformal mappings are generalized to $p$-sheeted conformal mappings of a multiply connected domain with given singularities at given points of the domain. Concrete estimates for certain functionals are obtained for an annulus. 
@article{MZM_1978_23_2_a9,
     author = {Yu. E. Alenitsyn},
     title = {Some extremal properties of conformal mappings of a~multiply connected domain onto canonical $p$-sheeted surfaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {261--270},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_2_a9/}
}
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Yu. E. Alenitsyn. Some extremal properties of conformal mappings of a~multiply connected domain onto canonical $p$-sheeted surfaces. Matematičeskie zametki, Tome 23 (1978) no. 2, pp. 261-270. http://geodesic.mathdoc.fr/item/MZM_1978_23_2_a9/