Geodesic
The Vuorinen problem on the maximum of the conformal module
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 120-134
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

A problem on the maximum of the conformal module over a family of doubly connected domains in the unit disk, being a hyperbolic analog of the Teichmüller problem, is solved. The cases when the desired maximum is expressed in elliptic functions are showed. 
@article{ZNSL_2012_404_a6,
     author = {E. G. Emel'yanov and G. V. Kuz'mina},
     title = {The {Vuorinen} problem on the maximum of the conformal module},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {120--134},
     year = {2012},
     volume = {404},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_404_a6/}
}
TY  - JOUR
AU  - E. G. Emel'yanov
AU  - G. V. Kuz'mina
TI  - The Vuorinen problem on the maximum of the conformal module
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2012
SP  - 120
EP  - 134
VL  - 404
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2012_404_a6/
LA  - en
ID  - ZNSL_2012_404_a6
ER  - 
%0 Journal Article
%A E. G. Emel'yanov
%A G. V. Kuz'mina
%T The Vuorinen problem on the maximum of the conformal module
%J Zapiski Nauchnykh Seminarov POMI
%D 2012
%P 120-134
%V 404
%U http://geodesic.mathdoc.fr/item/ZNSL_2012_404_a6/
%G en
%F ZNSL_2012_404_a6
E. G. Emel'yanov; G. V. Kuz'mina. The Vuorinen problem on the maximum of the conformal module. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 120-134. http://geodesic.mathdoc.fr/item/ZNSL_2012_404_a6/

[1] G. V. Kuzmina, “Moduli semeistv krivykh i kvadratichnye differentsialy.”, Trudy Mat. in-ta im. V. A. Steklova AN SSSR, 139, 1980, 3–241 | MR | Zbl

[2] A. Yu. Solynin, M. Vuorinen, “Extremal problems and symmetrization for plane ring domains”, Trans. Amer. Math. Soc., 348 (1999), 4095–4112 | DOI | MR

[3] A. Yu. Solynin, “Moduli i ekstremalno-metricheskie problemy”, Algebra i analiz, 11:1 (1999), 3–86 | MR | Zbl

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

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

[6] A. Yu. Solynin, Ob ekstremalnom razbienii ploskosti ili kruga na dve nenalegayuschie oblasti, Deponirovano v VINITI, No 7800-83, Kubanskii un-t, Krasnodar, 1984, 16 pp.