Abstract
We study two extremal problems for the product of powers of conformal radii of symmetric disjoint domains.
Similar content being viewed by others
References
M. A. Lavrent’ev, “On the theory of conformal mappings,” Tr. Fiz.-Mat. Inst. Akad. Nauk SSSR, 5, 159–245 (1934).
G. M. Goluzin, Geometric Theory of Functions of Complex Variables [in Russian], Nauka, Moscow (1966).
N. A. Lebedev, Principle of Areas in the Theory of Univalent Functions [in Russian], Nauka, Moscow (1975).
G. V. Kuz’mina, Moduli of Families of Curves and Quadratic Differentials [in Russian], Nauka, Leningrad (1980).
J. A. Jenkins, Univalent Functions and Conformal Mappings, Springer-Verlag, Berlin (1958).
V. N. Dubinin, Method of Symmetrization in the Geometric Theory of Functions [in Russian], Doctoral Degree Thesis (Phyics and Mathematics), Vladivostok (1988).
G. P. Bakhtina, Variational Methods and Quadratic Differentials in Problems of Disjoint Domains [in Russian], Author’s Abstract of the Candidate Degree Thesis (Physics and Mathematics), Kiev (1974).
V. N. Dubinin, “Separating transformation of domains and problems of extremal decompositions,” Zap. Nauch. Semin. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR, 168, 48–66 (1988).
E. G. Emel’yanov, “Relationship between two problems of extremal decomposition,” Zap. Nauch. Semin. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR, 160, 91–98 (1987).
G. P. Bakhtina, “On conformal radii of symmetric disjoint domains,” in: Contemporary Problems of Real and Complex Analysis [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1984), pp. 21–27.
J. A. Jenkins, “Some uniqueness results in the theory of symmetrization,” Ann. Math., 61, No. 1, 106–115 (1955).
W. K. Hayman, Multivalent Functions, Cambridge Univ. Press, Cambridge (1994).
P. L. Duren and M. Schiffer, “A variational method for functions schlicht in an annulus,” Arch. Rat. Mech. Anal., 9, 260–272 (1962).
M. Schiffer, “A method of variation within the family of simple functions,” Proc. London Math. Soc., 44, 432–449 (1938).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 2, pp. 179–185, February, 1997.
Rights and permissions
About this article
Cite this article
Bakhtina, G.P., Bakhtin, A.K. On extremal problems for symmetric disjoint domains. Ukr Math J 49, 197–203 (1997). https://doi.org/10.1007/BF02486435
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02486435