Abstract
Within the geometric theory of functions, we study one of the classical problems of extreme decomposition of a complex plane.
Similar content being viewed by others
References
V. N. Dubinin, “The method of symmetrization in the geometric theory of functions of a complex variable,” Uspekhi Mat. Nauk, 49, No. 1 (295), 3–76 (1994).
V. N. Dubinin, “A separating transformation of domains and problems of extreme decomposition,” Zap. Nauch. Sem. Leningr. Otd. Mat. Inst. AN SSSR, 168, 48–66 (1988).
V. N. Dubinin, Condenser Capacities and Symmetrization in Geometric Function Theory, Birkhäuser, Springer, Basel, 2014.
A. K. Bakhtin, G. P. Bakhtina, and Yu. B. Zelinskii, Topological Algebraic Structures and Geometric Methods in Complex Analysis [in Russian], Inst. Math. of the NAS of Ukraine, Kiev, 2008.
L. V. Kovalev, “To the problem of extreme decomposition with free poles on a circumference,” Dal’nevost. Mat. Sborn., 2, 96–98 (1996).
A. K. Bakhtin, I. V. Denega, “Addendum to a theorem on extremal decomposition of the complex plane,” Bull. de la Société des Sciences et des Lettres de Lódź, Rech. sur les Déform., LXII, No. 2, 83–92 (2012).
M. A. Lavrent’ev, “To the theory of conformal mappings,” Trudy Fiz.-Mat. Inst. AN SSSR, 5, 159–245 (1934).
G. M. Goluzin, Geometric Theory of Functions of a Complex Variable, Amer. Math. Soc., Providence, RI, 1969.
J. A. Jenkins, Univalent Functions and Conformal Mappings, Springer, Berlin, 1958.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Ukrains’ki˘ı Matematychny˘ı Visnyk, Vol. 13, No. 1, pp. 68–75, January–March, 2016.
Rights and permissions
About this article
Cite this article
Bakhtin, A.K., Vygivska, L.V. & Denega, I.V. Inequalities for the internal radii of non-overlapping domains. J Math Sci 220, 584–590 (2017). https://doi.org/10.1007/s10958-016-3201-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-016-3201-7