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 
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/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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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