Geodesic
Problems on the maximum of a conformal invariant in the presence of a high degree of symmetry
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 26, Tome 392 (2011), pp. 146-158 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The problem on the maximum of the conformal invariant $$ 2\pi\sum_{k=1}^nM(D_k,a_k)-\frac2{n-1}\prod_{1\leq k<l\leq n}|a_k-a_l|, $$ for all systems of points $\{a_1,\dots,a_n\}$ and all systems $\{D_1,\dots,D_n\}$ of nonoverlapping simply connected domains satisfying the condition $a_k\in D_k$, $k=1,\dots,n$, is investigated. Here $M(D,a)$ is the reduced module of a domain $D$ with respect to a point $a\in D $. It is assumed that $n$ is even and systems of points $a_1,\dots,a_n$ under consideration have a high degree of symmetry. 
@article{ZNSL_2011_392_a6,
     author = {G. V. Kuz'mina},
     title = {Problems on the maximum of a~conformal invariant in the presence of a~high degree of symmetry},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {146--158},
     year = {2011},
     volume = {392},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_392_a6/}
}
TY  - JOUR
AU  - G. V. Kuz'mina
TI  - Problems on the maximum of a conformal invariant in the presence of a high degree of symmetry
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2011
SP  - 146
EP  - 158
VL  - 392
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2011_392_a6/
LA  - ru
ID  - ZNSL_2011_392_a6
ER  - 
%0 Journal Article
%A G. V. Kuz'mina
%T Problems on the maximum of a conformal invariant in the presence of a high degree of symmetry
%J Zapiski Nauchnykh Seminarov POMI
%D 2011
%P 146-158
%V 392
%U http://geodesic.mathdoc.fr/item/ZNSL_2011_392_a6/
%G ru
%F ZNSL_2011_392_a6
G. V. Kuz'mina. Problems on the maximum of a conformal invariant in the presence of a high degree of symmetry. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 26, Tome 392 (2011), pp. 146-158. http://geodesic.mathdoc.fr/item/ZNSL_2011_392_a6/

[1] G. V. Kuzmina, “Metody geometricheskoi teorii funktsii”, Algebra i analiz, 9:5 (1997), 1–50 | MR | Zbl

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

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

[4] E. G. Emelyanov, “K zadache o maksimume proizvedeniya stepenei konformnykh radiusov nenalegayuschikh oblastei”, Zap. nauchn. semin. POMI, 286, 2002, 103–114 | MR | Zbl

[5] E. G. Emelyanov, “Konformno-invariantnye funktsionaly na rimanovoi sfere”, Zap. nauchn. semin. POMI, 276, 2001, 134–154 | MR | Zbl

[6] G. V. Kuzmina, “K zadache o maksimume proizvedeniya konformnykh radiusov nenalegayuschikh oblastei”, Zap. nauchn. semin. POMI, 100, 1980, 131–145 | MR | Zbl

[7] S. I. Fedorov, “O maksimume odnogo konformnogo invarianta v zadache o nenalegayuschikh oblastyakh”, Zap. nauchn. semin. POMI, 112, 1981, 172–183 | MR | Zbl

[8] G. V. Kuzmina, “K voprosu ob ekstremalnom razbienii rimanovoi sfery”, Zap. nauchn. semin. POMI, 185, 1990, 72–95 | MR

[9] 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

[10] E. G. Emelyanov, “K zadacham ob ekstremalnom razbienii”, Zap. nauchn. semin. POMI, 154, 1986, 76–89 | MR | Zbl

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

[12] L. I. Kolbina, “Nekotorye ekstremalnye zadachi v konformnom otobrazhenii”, Dokl. AN SSSR, 84 (1952), 865–868 | MR | Zbl