Extremal problems on the generalized (n, d)-equiangular system of points

A. Targonskii

doi:10.2478/auom-2014-0044

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Extremal problems on the generalized (n, d)-equiangular system of points

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 22 (2014): Issue 2 (June 2014)

By: A. Targonskii

Open Access

|Oct 2015

Abstract

The paper of Lavrent’ev [1] was the beginning of geometrical theory of functions of the complex variable. He solved a problem on the product of conformal radiuses of two non-overlapping domains. In many papers (see [2] – [13]) the Lavrent’ev’s result are generalized. In this paper are obtained the new results of this direction.

References

[1] Lavrent’ev M. A., On the theory of conformal mappings, Tr. Fiz.-Mat. Inst. Akad. Nauk SSSR, 5, 159-245 (1934).
Search in Google Scholar
[2] Goluzin G. M., Geometric Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1966).
Search in Google Scholar
[3] Bakhtina G. P., Variational Methods and Quadratic Differentials in Problems for Disjoint Domains [in Russian], Author’s Abstract of the Candidate-Degree Thesis (Physics and Mathematics), Kiev (1975).
Search in Google Scholar
[4] Kuz’mina G. V., Problem of extremal division of a Riemann sphere, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Ros. Akad. Nauk, 276, 253-275 (2001).
Search in Google Scholar
[5] Hayman W. K., Multivalent Functions, Cambridge University, Cambridge (1958).
Search in Google Scholar
[6] Dubinin V. N., Separating transformation of domains and problems of extremal division, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Ros. Akad. Nauk, 168, 48–66 (1988).
Search in Google Scholar
[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 p.
Search in Google Scholar
[8] Dubinin V. N., Asymptotic representation of the modulus of a degenerating condenser and some its applications, Zap. Nauchn. Sem. Peterburg. Otdel. Mat. Inst., 237, 56-73 (1997).
Search in Google Scholar
[9] Dubinin V. N., Method of symmetrization in the geometric theory of functions of a complex variable, Usp. Mat. Nauk, 49, No.1 (295), 3-76 (1994).10.1070/RM1994v049n01ABEH002002
Search in Google Scholar
[10] Emel’yanov E. G., On the problem of the maximum of the product of powers of conformal radii of disjoint domains, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Ros. Akad. Nauk, 286, 103-114 (2002).
Search in Google Scholar
[11] Bakhtin A. K., Sharp estimates for inner radii of systems of nonoverlap-ping domains and open sets, Ukr. Math. J., 59, No. 12, 1800-1818 (2007).
Search in Google Scholar
[12] Bakhtin A. K., Inequalities for the inner radii of nonoverlapping domains and open sets, Ukr. Math. J., 61, No. 5, 716-733 (2009).
Search in Google Scholar
[13] Bakhtin A. K. and Targonskii A. L., Generalized (n, d)-ray systems of points and inequalities for nonoverlapping domains and open sets, Ukr. Math. J., 63, No. 7, 716-733 (2011).
Search in Google Scholar
[14] Bakhtin A. K. and Targonskii A. L., Extremal problems and quadratic differentials, Nonlin. Oscillations, 8, No. 3, 296-301 (2005).
Search in Google Scholar
[15] Targonskii A. L., Extremal problems of partially nonoverlapping domains on a Riemann sphere, Dopov. Nats. Akad. Nauk Ukr., No. 9, 31-36 (2008).
Search in Google Scholar
[16] Jenkins J. A., Univalent Functions and Conformal Mapping, Springer, Berlin (1958).10.1007/978-3-662-34447-7
Search in Google Scholar