Geodesic
The symmetrization method in problems on nonoverlapping domains
Sbornik. Mathematics, Tome 56 (1987) no. 1, pp. 107-119

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A new approach to the use of symmetrization is considered. Sterner symmetrization is taken as the main tool. An arbitrary symmetrization transformation connected with a given quadratic differential $Q(z)dz^2$ is obtained by successive application of the mappng $\zeta=\int Q^{1/2}(z)\,dz$ and Steiner symmetrization. As a consequence of the main theorem, the corresponding results of Lavrent'ev, Goluzin, Jenkins, and others are refined and generalized to the case of domains of arbitrary connectivity (not necessarily having a filling). Bibliography: 21 titles. 
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     author = {V. N. Dubinin},
     title = {The symmetrization method in problems on nonoverlapping domains},
     journal = {Sbornik. Mathematics},
     pages = {107--119},
     publisher = {mathdoc},
     volume = {56},
     number = {1},
     year = {1987},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1987_56_1_a6/}
}
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V. N. Dubinin. The symmetrization method in problems on nonoverlapping domains. Sbornik. Mathematics, Tome 56 (1987) no. 1, pp. 107-119. http://geodesic.mathdoc.fr/item/SM_1987_56_1_a6/