The dependence of values of functionals occurring in some extremal decomposition problems on the location of the poles of the associated quadratic differentials is established. The proof is based on an analysis of geometric properties of trajectories of two quadratic differentials.
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J. A. Jenkins, “On the existence of certain general extremal mappings. I, II,” Ann. Math. (2), 66, 440–453 (1957); Tohoku Math. J. (2), 45, No. 2, 249–257 (1993).
G. V. Kuz’mina, “Moduli of families of curves and quadratic differentials,” Trudy Matem. Inst. im. V. A. Steklova AN SSSR, 139, 1–243 (1980).
E. G. Emel’yanov and G. V. Kuz’mina, “Theorems on the extremal decomposition in a family of systems of domains of various types,” Zap. Nauchn. Semin. POMI, 237, 74–104 (1997).
A. Yu. Solynin, “Moduli and extremal metric problems,” Algebra Analiz, 11, No. 1, 3–86 (1999).
J. A. Jenkins, “On the mixed problem for extremal decompositions,” Indiana Math. J., 49, No. 3, 891–896 (2000).
G. V. Kuz’mina, “Methods of geometric function theory,” Algebra Analiz, 9, No. 5, 1–60 (1997).
U. Pirl, “Über die geometrical Gestalt eines Extremalkontinuums aus der Theorie der konformen Abbildungen,” Math. Nachr., 39, Nos. 4–6, 297–312 (1969).
E. G. Emel’yanov and G. V. Kuz’mina, “The Vuorinen problem on the maximum of the conformal modulus,” Zap. Nauchn. Semin. POMI, 404, 120–134 (2012).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 418, 2013, pp. 90–104.
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Emel’yanov, E.G. Tangency Conditions for Trajectories of Two Quadratic Differentials. J Math Sci 200, 568–576 (2014). https://doi.org/10.1007/s10958-014-1945-5
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DOI: https://doi.org/10.1007/s10958-014-1945-5