A problem on the maximum of the conformal module in a family of doubly connected domains in the unit disk, which is a hyperbolic analog of the Teichmüller problem, is solved. The cases where the maximum in question is expressed in terms of elliptic functions are established. Bibliography: 6 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 404, 2012, pp. 120–134.
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Emel’yanov, E.G., Kuz’mina, G.V. The Vuorinen problem on the maximum of the conformal module. J Math Sci 193, 66–74 (2013). https://doi.org/10.1007/s10958-013-1434-2
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DOI: https://doi.org/10.1007/s10958-013-1434-2