Geodesic
About polarization with respect to hypersphere
Dalʹnevostočnyj matematičeskij žurnal, Tome 5 (2004) no. 1, pp. 22-29.

Voir la notice de l'article provenant de la source Math-Net.Ru

Polarization with respect to hypersphere is expressed with the help of conformal mappings through polarization of flat sets with respect to a straight line. It is formulated continuous (partial) simmetrization with respect to hypersphere in euclidean $n$-space. As an application of the new representation of hypersphere-polarization the non-increasing of the conformal capacity of condenser is proved. 
@article{DVMG_2004_5_1_a3,
     author = {E. V. Kostyuchenko and E. G. Prilepkina},
     title = {About polarization with respect to hypersphere},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {22--29},
     publisher = {mathdoc},
     volume = {5},
     number = {1},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2004_5_1_a3/}
}
TY  - JOUR
AU  - E. V. Kostyuchenko
AU  - E. G. Prilepkina
TI  - About polarization with respect to hypersphere
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2004
SP  - 22
EP  - 29
VL  - 5
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2004_5_1_a3/
LA  - ru
ID  - DVMG_2004_5_1_a3
ER  - 
%0 Journal Article
%A E. V. Kostyuchenko
%A E. G. Prilepkina
%T About polarization with respect to hypersphere
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2004
%P 22-29
%V 5
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2004_5_1_a3/
%G ru
%F DVMG_2004_5_1_a3
E. V. Kostyuchenko; E. G. Prilepkina. About polarization with respect to hypersphere. Dalʹnevostočnyj matematičeskij žurnal, Tome 5 (2004) no. 1, pp. 22-29. http://geodesic.mathdoc.fr/item/DVMG_2004_5_1_a3/

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

[2] V. Wolontis, “Properties of conformal invarians”, Amer. J. Math., 74:3 (1952), 587–606 | DOI | MR | Zbl

[3] V. N. Dubinin, “Capacities and geometric transformations of subsets in $n$-space”, Geometric and Functional Analysis, 3:4 (1993) | DOI | MR | Zbl

[4] A. Yu. Solynin, “Polyarizatsiya i funktsionalnye neravenstva”, Algebra i analiz, 8:6 (1996), 148–185 | MR | Zbl

[5] A. Yu. Solynin, “Nepreryvnaya simmetrizatsiya mnozhestv”, Zapiski nauchnykh seminarov LOMI, 185, 1990, 125–140

[6] E. G. Akhmedzyanova, “Simmetrizatsiya otnositelno gipersfery”, Dalnevostochnyi matematicheskii sbornik, 1, 1995, 40–50 | Zbl

[7] V. N. Dubinin, “Preobrazovanie kondensatorov v prostranstve”, Dokl. AN SSSR, 296:1 (1987), 18–20 | MR