Applications of the extremal metric method in its pure geometric aspect to problems on extremal decomposition are presented. Problems on the maxima of a certain weighted sum of the reduced modules of simply connected domains and of a related conformal invariant are solved. Bibliography: 13 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 383, 2010, pp. 126–143.
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Kuz’mina, G.V. The extremal metric method in the problem on the maximum of a conformal invariant. J Math Sci 178, 187–197 (2011). https://doi.org/10.1007/s10958-011-0538-9
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DOI: https://doi.org/10.1007/s10958-011-0538-9