Geodesic
An extremal problem on non-overlapping domains containing ellipse points
Eurasian mathematical journal, Tome 12 (2021) no. 4, pp. 82-91.

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An extremal problem of geometric function theory of a complex variable for the maximum of products of the inner radii on a system of $n$ mutually non-overlapping multiply connected domains $B_k$ containing the points $a_k$, $k=\overline{1,n}$, located on an arbitrary ellipse $\frac{x^2}{d^2}+\frac{y^2}{t^2}=1$ for which $d^2-t^2=1$, is solved. 
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Ya. V. Zabolotnii; I. V. Denega. An extremal problem on non-overlapping domains containing ellipse points. Eurasian mathematical journal, Tome 12 (2021) no. 4, pp. 82-91. http://geodesic.mathdoc.fr/item/EMJ_2021_12_4_a6/

[1] A. K. Bakhtin, G. P. Bakhtina, Yu. B. Zelinskii, “Topological-algebraic structures and geometric methods in complex analysis”, Zb. prats of the Inst. of Math. of NASU, 2008 (in Russian)

[2] A. Bakhtin, “Extremal decomposition of the complex plane with restrictions for free poles”, J. Math. Sci., 231:1 (2018), 1–15

[3] A. Bakhtin, “Separating transformation and extremal problems on nonoverlapping simply connected domains”, J. Math. Sci., 234:1 (2018), 1–13

[4] G. P. Bakhtina, Variational methods and quadratic differentials in problems of non-overlapping domains, PhD diss., Institute of Mathematics, Kiev, 1975 (in Russian)

[5] I. V. Denega, Ya. V. Zabolotnii, “Estimates of products of inner radii of non-overlapping domains in the complex plane”, Complex Variables and Elliptic Equations, 62:11 (2017), 1611–1618

[6] I. Denega, Ya. Zabolotnii, “Problem on extremal decomposition of the complex plane”, An. St. Univ. Ovidius Constanta, 27:1 (2019), 61–77

[7] V. N. Dubinin, “The product of internal radii of “partially nonoverlapping” domains”, Questions in the metric theory of mappings and its application, Proc. Fifth Colloq. Quasiconformal Mappings, Generalizations Appl. (Donetsk, 1976), “Naukova Dumka”, Kiev, 1978, 24–31

[8] V. N. Dubinin, “Symmetrization method in geometric function theory of complex variables”, Russian Math. Surveys, 1 (1994), 1–79

[9] V. N. Dubinin, Condenser capacities and symmetrization in geometric function theory, Birkhäuser/Springer, Basel, 2014

[10] G. M. Goluzin, Geometric theory of functions of a complex variable, Amer. Math. Soc., Providence, R.I., 1969

[11] J. A. Jenkins, Univalent functions and conformal mapping, Publishing House of Foreign Literature, M., 1962 (in Russian)

[12] L. I. Kolbina, “Conformal mapping of the unit circle onto non-overlapping domains”, Bulletin of Leningrad University, 5 (1955), 37–43 (in Russian)

[13] E. V. Kostyuchenko, “The solution of one problem of extremal decomposition”, Dal'nevost. Mat. Zh., 2:1 (2001), 3–15

[14] L. V. Kovalev, “On three disjoint domains”, Dal'nevost. Mat. Zh., 1:1 (2000), 3–7

[15] G. V. Kuz'mina, “Problems of extremal decomposition of the Riemann sphere”, Zap. Nauchn. Sem. POMI, 276, 2001, 253–275 (in Russian)

[16] M. A. Lavrent'ev, “On the theory of conformal mappings”, Travaux Inst. Physico-Math. Stekloff, 5, Acad. Sci. USSR, L., 1934, 159–245 (in Russian)

[17] N. A. Lebedev, The area principle in the theory of univalent functions, Science, M., 1975 (in Russian)

[18] G. Polya, G. Szegö, Isoperimetric inequalities in mathematical physics, Princeton Univ. Press, Princeton, 1951

[19] P. M. Tamrazov, “Extremal conformal mappings and poles of quadratic differentials”, Izv. Akad. Nauk SSSR, Ser. Mat., 32:5 (1968), 1033–1043

[20] Ya. Zabolotnii, I. Denega, “On conformal radii of non-overlapping simply connected domains”, International Journal of Advanced Research in Mathematics, 11:11 (2018), 1–7