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

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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. 
@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},
     publisher = {mathdoc},
     volume = {337},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_337_a7/}
}
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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/