Geodesic
Generalized condensers and the asymptotics of their capacities under degeneration of some plates
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 19, Tome 302 (2003), pp. 38-51 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

This note presents the simplest properties of the conformal capacity of generalized condensers concentrated on domains of the Riemann sphere. The asymptotic formula for the capacity of a generalized condenser as some of its plates contract to points is derived. 
@article{ZNSL_2003_302_a2,
     author = {V. N. Dubinin},
     title = {Generalized condensers and the asymptotics of their capacities under degeneration of some plates},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {38--51},
     year = {2003},
     volume = {302},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_302_a2/}
}
TY  - JOUR
AU  - V. N. Dubinin
TI  - Generalized condensers and the asymptotics of their capacities under degeneration of some plates
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2003
SP  - 38
EP  - 51
VL  - 302
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2003_302_a2/
LA  - ru
ID  - ZNSL_2003_302_a2
ER  - 
%0 Journal Article
%A V. N. Dubinin
%T Generalized condensers and the asymptotics of their capacities under degeneration of some plates
%J Zapiski Nauchnykh Seminarov POMI
%D 2003
%P 38-51
%V 302
%U http://geodesic.mathdoc.fr/item/ZNSL_2003_302_a2/
%G ru
%F ZNSL_2003_302_a2
V. N. Dubinin. Generalized condensers and the asymptotics of their capacities under degeneration of some plates. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 19, Tome 302 (2003), pp. 38-51. http://geodesic.mathdoc.fr/item/ZNSL_2003_302_a2/

[1] G. Polia, G. Sege, Izoperimetricheskie neravenstva v matematicheskoi fizike, M., 1962 | MR

[2] Ya. S. Soibelman, “Asimptotika ëmkosti kondensatora s plastinami proizvolnoi formy”, Sib. mat. zh., 25:6 (1984), 167–181 | MR | Zbl

[3] R. Kühnau, “Randeffekte beim elektrostatischen kondensator”, Zap. nauchn. semin. POMI, 254, 1998, 132–144 | MR

[4] L. V. Ahlfors, A. Beurling, “Conformal invariants and function-theoretic nullsets”, Acta. Math., 83:1–2 (1950), 101–129 | MR | Zbl

[5] V. K. Kheiman, Mnogolistnye funktsii, M., 1960

[6] Dzh. Dzhenkins, Odnolistnye funktsii i konformnye otobrazheniya, M., 1962

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

[8] V. N. Dubinin, “Privedënnye moduli otkrytykh mnozhestv v teorii analiticheskikh funktsii”, Dokl. RAN, 363:6 (1998), 731–734 | MR | Zbl

[9] V. N. Dubinin, N. V. Eirikh, “Obobschennyi privedënnyi modul”, Dalnevost. mat. zh., 3:2 (2002), 150–164 | MR

[10] G. V. Kuzmina, “Metody geometricheskoi teorii funktsii, I, II”, Algebra i analiz, 9:3 (1997), 41–103 | MR

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

[12] A. Vasil'ev, “Moduli of families of curves for conformal and quasiconformal mappings”, Lect. Notes in Math., 1788, 2002 | MR

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

[14] P. Duren, J. Pfaltzgraff, E. Thurman, “Physical interpretation and further properties of Robin capacity”, Algebra i analiz, 9:3 (1997), 211–219 | MR | Zbl

[15] V. M. Miklyukov, “O nekotorykh granichnykh zadachakh teorii konformnykh otobrazhenii”, Sib. mat. zh., 18:5 (1977), 1111–1124 | MR | Zbl

[16] J. Hersch, “On the reflection principle and some elementary ratios of conformal radii”, J. Anal. Math., 44 (1984/85), 251–268 | DOI | MR

[17] D. Gaier, W. Hayman, “On the computation of modules of long quadrilaterals”, Constr. Approx., 7 (1991), 453–467 | DOI | MR | Zbl

[18] V. N. Dubinin, “Asimptotika modulya vyrozhdayuschegosya kondensatora i nekotorye eë primeneniya”, Zap. nauchn. semin. POMI, 237, 1997, 56–73 | MR | Zbl

[19] V. N. Dubinin, L. V. Kovalëv, “Privedënnyi modul kompleksnoi sfery”, Zap. nauchn. semin. POMI, 254, 1998, 76–94 | MR