Geodesic
The Vuorinen problem on the maximum of the conformal module
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 120-134

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A problem on the maximum of the conformal module over a family of doubly connected domains in the unit disk, being a hyperbolic analog of the Teichmüller problem, is solved. The cases when the desired maximum is expressed in elliptic functions are showed. 
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     author = {E. G. Emel'yanov and G. V. Kuz'mina},
     title = {The {Vuorinen} problem on the maximum of the conformal module},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_404_a6/}
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E. G. Emel'yanov; G. V. Kuz'mina. The Vuorinen problem on the maximum of the conformal module. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 120-134. http://geodesic.mathdoc.fr/item/ZNSL_2012_404_a6/