Geodesic
About one problem on extremal decomposition
Problemy analiza, Tome 10 (2021) no. 3, pp. 141-150.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper, we consider an open problem of finding the maximum of product of inner radii of mutually non-overlapping domains with respect to the points of the unit circle on a certain positive degree $\gamma$ of the inner radius of the domain with respect to the origin, moreover, the domain containing origin does not intersect with other domains.
Keywords: inner radius of the domain, mutually non-overlapping domains, the Green function, quadratic differential, the Dubinin problem. 
@article{PA_2021_10_3_a10,
     author = {Ya. Zabolotnii and I. Denega},
     title = {About one problem on extremal decomposition},
     journal = {Problemy analiza},
     pages = {141--150},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2021_10_3_a10/}
}
TY  - JOUR
AU  - Ya. Zabolotnii
AU  - I. Denega
TI  - About one problem on extremal decomposition
JO  - Problemy analiza
PY  - 2021
SP  - 141
EP  - 150
VL  - 10
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2021_10_3_a10/
LA  - en
ID  - PA_2021_10_3_a10
ER  - 
%0 Journal Article
%A Ya. Zabolotnii
%A I. Denega
%T About one problem on extremal decomposition
%J Problemy analiza
%D 2021
%P 141-150
%V 10
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2021_10_3_a10/
%G en
%F PA_2021_10_3_a10
Ya. Zabolotnii; I. Denega. About one problem on extremal decomposition. Problemy analiza, Tome 10 (2021) no. 3, pp. 141-150. http://geodesic.mathdoc.fr/item/PA_2021_10_3_a10/

[1] Bakhtin A. K., “Estimates of inner radii for pairwise non-overlapping domains”, Zb. prats of the Inst. of Math. of NASU, 14:1 (2017), 25–33 | Zbl

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

[3] Bakhtin A. K., Denega I. V., “Addendum to a theorem on extremal decomposition of the complex plane”, Bulletin de la sociétédes sciences et des lettres de Lódź, Recherches sur les déformations, 62:2 (2012), 83–92 | MR | Zbl

[4] Bakhtin A. K., Denega I. V., “Inequalities for the inner radii of nonoverlapping domains”, Ukr. Math. J., 71 (2019), 1138–1145 | DOI | MR | Zbl

[5] Bakhtin A. K., Denega I. V., “Extremal decomposition of the complex plane with free poles”, J. Math. Sci., 246:1 (2020), 1–17 | DOI | MR | Zbl

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

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

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

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

[10] Dubinin V. N., Condenser capacities and symmetrization in geometric function theory, Birkhäuser/Springer, Basel, 2014 | DOI | MR | Zbl

[11] Hayman V., Multivalent functions, Cambridge University Press, Cambridge, 1958 | MR | Zbl

[12] Jenkins J., Univalent functions and conformal mapping, Publishing House of Foreign Literature, M., 1962, 256 pp. (in Russian) | DOI | MR

[13] Kolbina L. I., “Conformal mapping of a unit circle onto nonoverlapping domains”, Vestn. Lenin. Univ., 5 (1955), 37–43 (in Russian) | MR | Zbl

[14] Kovalev L. V., “On the problem of extremal decomposition with free poles on a circle”, Dal'nevost. Mat. Zh., 1996, no. 2, 96–98 (in Russian) | MR | Zbl

[15] Lavrent'ev M. A., “On the theory of conformal mappings”, Tr. Sci. Inst An USSR, 5 (1934), 159–245 (in Russian)

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

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

[18] Zabolotnii Ya. V., “Some application of the method of separating transformation in one problem on nonoverlapping domains”, Dopov. Nac. akad. nauk Ukr., 2011, no. 9, 11–14 | MR | Zbl

[19] Zabolotnii Ya., Denega I., “On Conformal Radii of Non-Overlapping Simply Connected Domains”, International Journal of Advanced Research in Mathematics, 11:11 (2018), 1–7 | DOI

[20] Zabolotnii Ya., Dvorak I., “Some evaluation of maximum of the product of conformal radii for pairwaise nonoverlapping domains”, Lobachevskii Journal of Mathematics, 38:6 (2017), 554–559 | DOI | MR | Zbl