Geodesic
The method of extremal metric in the problem on the maximum of a~conformal invariant
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 25, Tome 383 (2010), pp. 126-143

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Applications of an extremal metric approach to the 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. Bibl. 13 titles. 
@article{ZNSL_2010_383_a8,
     author = {G. V. Kuz'mina},
     title = {The method of extremal metric in the problem on the maximum of a~conformal invariant},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {126--143},
     publisher = {mathdoc},
     volume = {383},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_383_a8/}
}
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G. V. Kuz'mina. The method of extremal metric in the problem on the maximum of a~conformal invariant. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 25, Tome 383 (2010), pp. 126-143. http://geodesic.mathdoc.fr/item/ZNSL_2010_383_a8/