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Zap. Nauchn. Sem. POMI, 2003, Volume 302, Pages 38–51 (Mi znsl917)  

This article is cited in 23 scientific papers (total in 23 papers)

Generalized condensers and the asymptotics of their capacities under degeneration of some plates

V. N. Dubinin

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences

Abstract: 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.

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English version:
Journal of Mathematical Sciences (New York), 2005, 129:3, 3835–3842

Bibliographic databases:

UDC: 517.54
Received: 08.10.2003

Citation: V. N. Dubinin, “Generalized condensers and the asymptotics of their capacities under degeneration of some plates”, Analytical theory of numbers and theory of functions. Part 19, Zap. Nauchn. Sem. POMI, 302, POMI, St. Petersburg, 2003, 38–51; J. Math. Sci. (N. Y.), 129:3 (2005), 3835–3842

Citation in format AMSBIB
\by V.~N.~Dubinin
\paper Generalized condensers and the asymptotics of their capacities under degeneration of some plates
\inbook Analytical theory of numbers and theory of functions. Part~19
\serial Zap. Nauchn. Sem. POMI
\yr 2003
\vol 302
\pages 38--51
\publ POMI
\publaddr St.~Petersburg
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 129
\issue 3
\pages 3835--3842

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    This publication is cited in the following articles:
    1. V. N. Dubinin, N. V. Eyrikh, “Some applications of generalized condensers to analytic function theory”, J. Math. Sci. (N. Y.), 133:6 (2006), 1634–1647  mathnet  crossref  mathscinet  zmath  elib  elib
    2. V. N. Dubinin, E. G. Prilepkina, “O sokhranenii obobschennogo privedennogo modulya pri geometricheskikh preobrazovaniyakh ploskikh oblastei”, Dalnevost. matem. zhurn., 6:1-2 (2005), 39–56  mathnet  elib
    3. V. N. Dubinin, “Capacities of condensers, generalizations of Grötzsch Lemmas, and symmetrization”, J. Math. Sci. (N. Y.), 143:3 (2007), 3053–3068  mathnet  crossref  mathscinet  zmath  elib  elib
    4. V. N. Dubinin, E. G. Prilepkina, “On variational principles of conformal mappings”, St. Petersburg Math. J., 18:3 (2007), 373–389  mathnet  crossref  mathscinet  zmath  elib
    5. V. N. Dubinin, V. Yu. Kim, “Distortion theorems for bounded regular functions in the disk”, J. Math. Sci. (N. Y.), 150:3 (2008), 2018–2026  mathnet  crossref  elib  elib
    6. Dubinin V.N., Karp D.B., “Generalized condensers and distortion theorems for conformal mappings of planar domains”, Interaction of Analysis and Geometry, Contemporary Mathematics Series, 424, 2007, 33–51  crossref  mathscinet  zmath  isi
    7. V. N. Dubinin, D. A. Kirillova, “On extremal decomposition problems”, J. Math. Sci. (N. Y.), 157:4 (2009), 573–583  mathnet  crossref  zmath
    8. V. N. Dubinin, D. B. Karp, V. A. Shlyk, “Izbrannye zadachi geometricheskoi teorii funktsii i teorii potentsiala”, Dalnevost. matem. zhurn., 8:1 (2008), 46–95  mathnet  elib
    9. V. N. Dubinin, “Emkosti kondensatorov i printsipy mazhoratsii v geometricheskoi teorii funktsii kompleksnogo peremennogo [Itogovyi nauchnyi otchet po mezhdistsiplinarnomu integratsionnomu proektu SO RAN: “Razrabotka teorii i vychislitelnoi tekhnologii resheniya obratnykh i ekstremalnykh zadach s prilozheniem v matematicheskoi fizike i gravimagnitorazvedke”]”, Sib. elektron. matem. izv., 5 (2008), 465–482  mathnet  mathscinet
    10. Dubinin V.N., Karp D., “Capacities of certain plane condensers and sets under simple geometric transformations”, Complex Variables and Elliptic Equations, 53:6 (2008), 607–622  crossref  mathscinet  zmath  isi
    11. V. N. Dubinin, “Quadratic forms involving Green's and Robin functions”, Sb. Math., 200:10 (2009), 1439–1452  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. V. N. Dubinin, “On I. P. Mityuk's results on the the behavior of the inner radius of a domain and the condenser's capacity under regular mappings”, J. Math. Sci. (N. Y.), 166:2 (2010), 145–154  mathnet  crossref  elib
    13. Karp D., Prilepkina E., “Reduced Modulus with Free Boundary and its Applications”, Annales Academiae Scientiarum Fennicae-Mathematica, 34:2 (2009), 353–378  mathscinet  zmath  isi  elib
    14. V. N. Dubinin, “Emkosti kondensatorov i simmetrizatsiya v zadachakh ob ekstremalnom razbienii”, Dalnevost. matem. zhurn., 9:1-2 (2009), 84–93  mathnet  elib
    15. V. N. Dubinin, E. G. Prilepkina, “Distortion theorems for univalent meromorphic functions on an annulus”, Siberian Math. J., 51:2 (2010), 229–243  mathnet  crossref  mathscinet  isi  elib  elib
    16. V. N. Dubinin, D. A. Kirillova, “Nekotorye primeneniya ekstremalnykh razbienii v geometricheskoi teorii funktsii”, Dalnevost. matem. zhurn., 10:2 (2010), 130–152  mathnet  elib
    17. Dubinin V.N., Vuorinen M., “Robin functions and distortion theorems for regular mappings”, Math Nachr, 283:11 (2010), 1589–1602  crossref  mathscinet  zmath  isi  elib  scopus
    18. E. G. Prilepkina, “On composition principles for reduced moduli”, Siberian Math. J., 52:6 (2011), 1079–1091  mathnet  crossref  mathscinet  isi
    19. Pouliasis S., “Condenser Energy Under Holomorphic Motions”, Ill. J. Math., 55:3 (2011), 1119–1134  mathscinet  zmath  isi
    20. V. N. Dubinin, “Asymptotic Behavior of the Capacity of a Condenser as Some of Its Plates Contract to Points”, Math. Notes, 96:2 (2014), 187–198  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    21. V. N. Dubinin, “On the reduced modulus of the complex sphere”, Siberian Math. J., 55:5 (2014), 882–892  mathnet  crossref  mathscinet  isi
    22. J. Math. Sci. (N. Y.), 222:5 (2017), 645–689  mathnet  crossref  mathscinet
    23. Betsakos D., Kelgiannis G., Kourou M., Pouliasis S., “On the Asymptotic Behavior of Condenser Capacity Under Blaschke Products and Universal Covering Maps”, Proc. Amer. Math. Soc., 147:7 (2019), 2963–2973  crossref  isi
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