Inequality for the inner radii of symmetric non-overlapping domains

Authors

  • Aleksandr Bakhtin Institute of Mathematics, National Academy of Sciences of Ukraine
  • Liudmyla Vyhivska Institute of Mathematics, National Academy of Sciences of Ukraine
  • Iryna Denega Institute of Mathematics, National Academy of Sciences of Ukraine

DOI:

https://doi.org/10.26485/0459-6854/2018/68.2/3

Keywords:

inner radius of domain, non-overlapping domains, radial system of points, separating transformation, quadratic differential, Green’s function

Abstract

The paper deals with the problem stated  by V.N. Dubinin and earlier in different form by G.P. Bakhtina.

References

V. N. Dubinin, Symmetrization in the geometric theory of functions of a complex variable, Russian Mathematical Surveys 49(1) (1994), 1–79.

G.P. Bakhtina, On the conformal radii of symmetric nonoverlapping regions, Modern issues of material and complex analysis, K.: Inst. Math. of NAS of Ukraine, (1984), 21–27.

L. V. Kovalev, On the inner radii of symmetric nonoverlapping domains, Izv. Vyssh. Uchebn. Zaved. Mat. 6 (2000), 77–78.

L. V. Kovalev, On three nonoverlapping domains, Dal’nevost. Mat. Zh. 1 (2000), 3–7.

A. K. Bakhtin, G.P. Bakhtina, Yu. B. Zelinskii, Topological- Algebraic Structures and Geometric Methods in Complex Analysis, K.: Inst. Math. of NAS of Ukraine, 2008. (in Russian) L. V. Kovalev, To the ploblem of extremal decomposition with free poles on a circumference, Dalnevost. Mat. Sborn. 2 (1996), 96–98.

A. K. Bakhtin, I. V. Denega, Addendum to a theorem on extremal decomposition of the complex plane, Bulletin de la societe des sciences et des lettres de Lodz, Recherches sur les deformations 62, no. 2, (2012), 83–92.

A. K. Bakhtin, Estimates of inner radii for mutually disjoint domains, Zb. pr. In-t matem. of NAS of Ukraine 14, no. 1, (2017), 25–33.

A. K. Bakhtin, G.P. Bakhtina, I. V. Denega, Extremal decomposition of a complex plane with fixed poles, Zb. pr. In-t matem. of NAS of Ukraine 14, no. 1, (2017), 34–38.

J. A. Jenkins, Univalent Functions and Conformal Mappings, Berlin: Springer, 1962.

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Published

2019-04-26

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Articles