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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

It is proved that a meromorphic function that preserves the capacity of a plane condenser is univalent in the field of the condenser.
@article{ZNSL_2011_392_a2,
     author = {V. N. Dubinin},
     title = {On the preservation of conformal capacity under meromorphic functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {67--73},
     year = {2011},
     volume = {392},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_392_a2/}
}
TY  - JOUR
AU  - V. N. Dubinin
TI  - On the preservation of conformal capacity under meromorphic functions
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2011
SP  - 67
EP  - 73
VL  - 392
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2011_392_a2/
LA  - ru
ID  - ZNSL_2011_392_a2
ER  - 
%0 Journal Article
%A V. N. Dubinin
%T On the preservation of conformal capacity under meromorphic functions
%J Zapiski Nauchnykh Seminarov POMI
%D 2011
%P 67-73
%V 392
%U http://geodesic.mathdoc.fr/item/ZNSL_2011_392_a2/
%G ru
%F ZNSL_2011_392_a2
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/

[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