Abstract
Paper is devoted to one classic problem of geometric function theory on extremal decomposition of the complex plane. We consider a problem of maximization of product of inner radii of n non-overlapping domains.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. Dubinin, “Symmetrization method in geometric function theory of complex variables,” Russ. Math. Surv. 49 (1), 1–79 (1994).
V. Dubinin, Condenser Capacities and Symmetrization in Geometric Function Theory (Birkhäuser, Springer, Basel, 2014).
V. Dubinin, “Separating transformation of domains and problems on extremal decomposition,” J. Sov. Math. 53, 252–263 (1991).
L. Kovalev, “On the problem of extremal decomposition with free poles on a circle,” Dal’nevost. Mat. Sb. 2, 96–98 (1996).
G. Kuzmina, “Extremal metric method in problems of the maximum of product of powers of conformal radii of non-overlapping domains with free parameters,” J. Math. Sci. (N. Y.) 129, 3843–3851 (2005).
A. Bakhtin, G. Bakhtina, and Yu. Zelinskii, “Topological-algebraic structures and geometric methods in complex analysis,” Tr. Inst. Mat. NANU (2008).
Ja. Zabolotnij, “Application of separation transformation in one problem on non-overlapping domains,” Dopov. Nac. Akad. Nauk Ukr., No. 9, 11–14 (2011).
A. Bakhtin, I. Denega, “Addendum to a theorem on extremal decomposition of the complex plane,” Bull. Soc. Sci. Lett. Lódź, Recher. Déform. 62 (2), 83–92 (2012).
A. Bakhtin and I. Denega, “About one Dubinin’s problem,” Tr. Inst. Mat. NANU 10, 401–411 (2013).
Ja. Zabolotnij, “Determination of the maximum of a product of inner radii of pairwise nonoverlapping domains,” Dopov. Nac. Akad. Nauk Ukr., No. 3, 7–13 (2016).
A. Bakhtin, L. Vygivska, and I. Denega, “An inequalities for the inner radii of non-overlapping domains,” Ukr. Mat. Byull. 13, 68–75 (2016).
J. Jenkins, Univalent Functions and Conformal Mapping, Vol. 18 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge (Springer, Berlin, 1958).
K. Strebel, Quadratic Differentials (Springer, Berlin, Heidelberg, New York, 1984).
L. Kolbina, “Conformal mapping of the unit circle onto non-overlapping domains,” Byull. Leningr. Univ. 5, 37–43 (1955).
M. Lavrent’ev, “On the theory of conformal mappings,” Tr. Fiz. -Mat. Inst. Steklov 5, 159–245 (1934).
G. Goluzin, Geometric Theory of Functions of a Complex Variable (Am. Math. Soc., Providence, RI, 1969).
V. Hayman, Multivalent Functions (Cambridge Univ. Press, Cambridge, 1958).
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to V.Ya. Gutlyanskii on the occasion of his 75th birthday
Submitted by V. V. Zharinov
Rights and permissions
About this article
Cite this article
Bakhtin, A., Vygivska, L. & Denega, I. N-radial systems of points and problems for non-overlapping domains. Lobachevskii J Math 38, 229–235 (2017). https://doi.org/10.1134/S1995080217020044
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080217020044