Geodesic
On the maximum of product of conformal radii of nonverlapping domains in the circle
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 14, Tome 237 (1997), pp. 105-118

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Two problems on the extremal decomposition of the unit disk are considered. It is shown that the associated quadratic differentials in these problems have at least two distinct zeros on the unit circle. 
@article{ZNSL_1997_237_a8,
     author = {V. O. Kuznetsov},
     title = {On the maximum of product of conformal radii of nonverlapping domains in the circle},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {105--118},
     publisher = {mathdoc},
     volume = {237},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_237_a8/}
}
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V. O. Kuznetsov. On the maximum of product of conformal radii of nonverlapping domains in the circle. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 14, Tome 237 (1997), pp. 105-118. http://geodesic.mathdoc.fr/item/ZNSL_1997_237_a8/