Extremal problem on (2n, 2m – 1)-system points on the rays

Andrey Targonskii

doi:10.1515/auom-2016-0043

.blurhash-client-img { display: none !important; }

Extremal problem on (2n, 2m – 1)-system points on the rays

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 24 (2016): Issue 2 (June 2016)

By: Andrey Targonskii

Open Access

|Sep 2017

Abstract

In this work derivation of accurate estimate the production inner radius non-overlapping domains and open set. The problems arise such type in the first time in work [1]. It is late result this work generalize and strengthen in works [2 - 13]. In works [7, 8, 10] introduce the general systems points, the name n-radial systems points. In this work a success the draw generalize some results the work [7].

References

[1] M. A. Lavrent'ev, On the theory of conformal mappings, Tr. Fiz.-Mat. Inst. Akad. Nauk SSSR, 5, 159245 (1934).
Search in Google Scholar Back to article
[2] G. M. Goluzin, Geometric Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1966).
Search in Google Scholar Back to article
[3] G. P. Bakhtina, Variational Methods and Quadratic Di_erentials in Problems for Disjoint Domains [in Russian], Author's Abstract of the Candidate-Degree Thesis (Physics and Mathematics), Kiev (1975).
Search in Google Scholar Back to article
[4] V. N. Dubinin, Separating transformation of domains and problems of extremal division, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Ros. Akad. Nauk, 168, 4866 (1988). - 168. - P. 48 - 66.
Search in Google Scholar Back to article
[5] V. N. Dubinin, Method of symmetrization in the geometric theory of functions of a complex variable, Usp. Mat. Nauk, 49, No.1 (295), 376 (1994).10.1070/RM1994v049n01ABEH002002
Search in Google Scholar Back to article
[6] V. N. Dubinin, Asymptotic representation of the modulus of a degener- ating condenser and some its applications, Zap. Nauchn. Sem. Peterburg. Otdel. Mat. Inst., 237, 5673 (1997).
Search in Google Scholar Back to article
[7] Bakhtin, A. K., Bakhtina, G. P., Zelinskii, Yu. B., "Topological-algebraic structures and geometric methods in complex analysis," Proceedings of the Institute of Mathematics of NAS of Ukraine 73 (2008), 308 pp. (Rus- sian).
Search in Google Scholar Back to article
[8] O. K. Bakhtin, Inequalities for the inner radii of nonoverlapping domains and open sets, Ukr. Mat. Zh., 61, No. 5, 596610 (2009); English transla- tion: Ukr. Math. J., 61, No. 5, 716733 (2009).
Search in Google Scholar Back to article
[9] Dubinin, V. N., Capacities of condensers and symmetrization in geomet- ric function theory of complex variables, Dalnayka, Vladivostok, 2009 (Russian).
Search in Google Scholar Back to article
[10] A. K. Bakhtin and A. L. Targonskii, Extremal problems and quadratic di_erentials, Nelin. Kolyvannya, 8, No. 3, 298303 (2005); English trans- lation: Nonlin. Oscillations, 8, No. 3, 296301 (2005).
Search in Google Scholar Back to article
[11] A. L. Targonskii, Extremal problems of partially nonoverlapping domains on a Riemann sphere, Dopov. Nats. Akad. Nauk Ukr., No. 9, 3136 (2008).
Search in Google Scholar Back to article
[12] G. V. Kuz'mina, Problem of extremal division of a Riemann sphere, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Ros. Akad. Nauk, 276, 253275 (2001).
Search in Google Scholar Back to article
[13] E. G. Emel'yanov, On the problem of the maximum of the product of pow- ers of conformal radii of disjoint domains, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Ros. Akad. Nauk, 286, 103-114 (2002).
Search in Google Scholar Back to article
[14] W. K. Hayman, Multivalent Functions, Cambridge University, Cambridge (1958).
Search in Google Scholar Back to article
[15] J. A. Jenkins, Univalent Functions and Conformal Mapping, Springer, Berlin (1958).10.1007/978-3-642-88563-1
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.1515/auom-2016-0043 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

Journal RSS Feed

Language: English

Page range: 283 - 299

Submitted on: Jan 25, 2014

Accepted on: Feb 20, 2015

Published on: Sep 21, 2017

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

inner radius of domain,

quadratic differential,

piecewise-separating trans- formation,

the Green function,

radial systems of points,

logarithmic capacity,

variational formula.

Related subjects:

Mathematics,

General mathematics

© 2017 Andrey Targonskii, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 24 (2016): Issue 2 (June 2016)