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Zap. Nauchn. Sem. POMI, 2006, Volume 337, Pages 73–100 (Mi znsl183)  

This article is cited in 9 scientific papers (total in 9 papers)

Capacities of condensers, generalizations of Grötzsch Lemmas, and symmetrization

V. N. Dubinin

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

Abstract: Principles of symmetry and composition for the conformal capacity of generalized condensers are considered. Interrelations among these principles, the classical Grötzsch lemmas, and certain types of symmetrization are discussed. Applications to estimating the logarithmic and hyperbolic capacities of compacts and to extremal decomposition problems are presented. Bibliography: 27 titles.

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English version:
Journal of Mathematical Sciences (New York), 2007, 143:3, 3053–3068

Bibliographic databases:

UDC: 517.54
Received: 23.03.2005

Citation: V. N. Dubinin, “Capacities of condensers, generalizations of Grötzsch Lemmas, and symmetrization”, Analytical theory of numbers and theory of functions. Part 21, Zap. Nauchn. Sem. POMI, 337, POMI, St. Petersburg, 2006, 73–100; J. Math. Sci. (N. Y.), 143:3 (2007), 3053–3068

Citation in format AMSBIB
\Bibitem{Dub06}
\by V.~N.~Dubinin
\paper Capacities of condensers, generalizations of Gr\"otzsch Lemmas, and symmetrization
\inbook Analytical theory of numbers and theory of functions. Part~21
\serial Zap. Nauchn. Sem. POMI
\yr 2006
\vol 337
\pages 73--100
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl183}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2271958}
\zmath{https://zbmath.org/?q=an:1115.30023}
\elib{http://elibrary.ru/item.asp?id=9305275}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 143
\issue 3
\pages 3053--3068
\crossref{https://doi.org/10.1007/s10958-007-0191-5}
\elib{http://elibrary.ru/item.asp?id=13554480}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34248224637}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. V. N. Dubinin, D. A. Kirillova, “On extremal decomposition problems”, J. Math. Sci. (N. Y.), 157:4 (2009), 573–583  mathnet  crossref  zmath
    3. 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
    4. V. V. Vasin, V. N. Dubinin, V. G. Romanov, “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), 427–439  mathnet  elib
    5. 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
    6. D. A. Kirillova, “Univalent functions without common values”, Russian Math. (Iz. VUZ), 54:9 (2010), 74–76  mathnet  crossref  mathscinet  elib
    7. V. N. Dubinin, D. A. Kirillova, “Nekotorye primeneniya ekstremalnykh razbienii v geometricheskoi teorii funktsii”, Dalnevost. matem. zhurn., 10:2 (2010), 130–152  mathnet  elib
    8. V. N. Dubinin, “Geometric versions of Schwarz lemma and symmetrization”, J. Math. Sci. (N. Y.), 178:2 (2011), 150–157  mathnet  crossref
    9. S. I. Kalmykov, E. G. Prilepkina, “On the $p$-harmonic Robin radius in the Euclidean space”, J. Math. Sci. (N. Y.), 225:6 (2017), 969–979  mathnet  crossref  mathscinet
  • Записки научных семинаров ПОМИ
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