Geodesic
On quadratic differentials on multiply connected domains that are perfect squares
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 21, Tome 337 (2006), pp. 113-133 
E. G. Emel'yanov. On quadratic differentials on multiply connected domains that are perfect squares. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 21, Tome 337 (2006), pp. 113-133. http://geodesic.mathdoc.fr/item/ZNSL_2006_337_a7/
@article{ZNSL_2006_337_a7,
     author = {E. G. Emel'yanov},
     title = {On quadratic differentials on multiply connected domains that are perfect squares},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {113--133},
     year = {2006},
     volume = {337},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_337_a7/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The paper considers the problem on extremal decomposition of a multiply connected domain $G\subset\mathbb C$ in the case where the associated quadratic differential is a perfect square. It is shown that in the case considered, the value of the functional for this extremal decomposition is the least one in a certain class of decompositions. Bibliography: 10 titles.

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[5] J. A. Jenkins, “On mixed problems of extremal decompositions”, Indiana Math. J., 49:3 (2000), 391–396 | DOI | MR

[6] G. V. Kuzmina, “Moduli semeistv krivykh i kvadratichnye differentsialy”, Trudy MIAN, 139, 1980, 3–241 | MR

[7] K. Strebel, Quadratic differentials, Springer-Verlag, 1984 | MR

[8] A. Yu. Solynin, “Moduli i ekstremalno-metricheskie problemy”, Algebra i analiz, 11:1 (1999), 3–86 | MR | Zbl

[9] E. G. Emelyanov, G. V. Kuzmina, “Teoremy ob ekstremalnom razbienii v semeistvakh sistem oblastei razlichnykh tipov”, Zap. nauchn. semin. POMI, 237, 1997, 74–104 | MR

[10] V. O. Kuznetsov, “O svoistvakh konformnogo radiusa oblasti”, Zap. nauchn. semin. POMI, 276, 2001, 237–252 | MR | Zbl