On the preservation of conformal capacity under meromorphic functions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 26, Tome 392 (2011), pp. 67-73
V. N. Dubinin. On the preservation of conformal capacity under meromorphic functions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 26, Tome 392 (2011), pp. 67-73. http://geodesic.mathdoc.fr/item/ZNSL_2011_392_a2/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

It is proved that a meromorphic function that preserves the capacity of a plane condenser is univalent in the field of the condenser.

[1] W. K. Hayman, Multivalent functions, Cambridge Univ. Press, Cambridge, 1994 | MR | Zbl

[2] V. N. Dubinin, “Simmetrizatsiya v geometricheskoi teorii funktsii kompleksnogo peremennogo”, Uspekhi mat. nauk, 49:1 (1994), 3–76 | MR | Zbl

[3] T. Kubo, “Hyperbolic transfinite diameter and some theorems on analytic functions in an annulus”, J. Math. Soc. Japan, 10 (1958), 348–364 | DOI | MR | Zbl

[4] I. P. Mityuk, “Printsip simmetrizatsii dlya koltsa i nekotorye ego primeneniya”, Sib. mat. zhurn., 6 (1965), 1282–1291 | MR | Zbl

[5] I. P. Mityuk, “Nekotorye svoistva funktsii, regulyarnykh v mnogosvyaznoi oblasti”, Dokl. AN SSSR, 164 (1965), 495–498 | Zbl

[6] I. P. Mityuk, Simmetrizatsionnye metody i ikh primenenie v geometricheskoi teorii funktsii. Vvedenie v simmetrizatsionnye metody, Izd-vo Kubanskogo un-ta, Krasnodar, 1980

[7] I. P. Mityuk, Primenenie simmetrizatsionnykh metodov v geometricheskoi teorii funktsii, Izd-vo Kubanskogo un-ta, Krasnodar, 1985

[8] S. Pouliasis, “Condenser capacity and meromorphic functions”, Comput. methods and funct. theory, 11 (2011), 237–245 | DOI | MR | Zbl

[9] N. S. Landkof, Osnovy sovremennoi teorii potentsiala, M., 1966 | MR

[10] H. Kloke, “Some inequalities for the capacity of plane condensers”, Results Math., 9 (1986), 82–94 | DOI | MR | Zbl

[11] V. N. Dubinin, Emkosti kondensatorov i simmetrizatsiya v geometricheskoi teorii funktsii kompleksnogo peremennogo, Vladivostok, 2009

[12] T. Ransford, Potential theory in the complex plane, London Math. Soc. Student Texts, 28, Cambridge Univ. Press, 1995 | MR | Zbl