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Algebra i Analiz, 2006, Volume 18, Issue 3, Pages 39–62 (Mi aa73)  

This article is cited in 7 scientific papers (total in 7 papers)

On the occasion of the 100th anniversary of G. M. Golusin's birth

On variational principles of conformal mappings

V. N. Dubinin, E. G. Prilepkina

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

Abstract: Refinements and generalizations of the classical variational principles of conformal mappings are presented; mainly, they follow from potential theory and symmetrization. Part of the results can be viewed as properties of Robin functions and Robin capacities, and also as distortion theorems for univalent functions in finitely connected domains.

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English version:
St. Petersburg Mathematical Journal, 2007, 18:3, 373–389

Bibliographic databases:

MSC: 30C70, 30C85
Received: 22.02.2006

Citation: V. N. Dubinin, E. G. Prilepkina, “On variational principles of conformal mappings”, Algebra i Analiz, 18:3 (2006), 39–62; St. Petersburg Math. J., 18:3 (2007), 373–389

Citation in format AMSBIB
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\by V.~N.~Dubinin, E.~G.~Prilepkina
\paper On variational principles of conformal mappings
\jour Algebra i Analiz
\yr 2006
\vol 18
\issue 3
\pages 39--62
\mathnet{http://mi.mathnet.ru/aa73}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2255850}
\zmath{https://zbmath.org/?q=an:1146.30011}
\elib{http://elibrary.ru/item.asp?id=12894791}
\transl
\jour St. Petersburg Math. J.
\yr 2007
\vol 18
\issue 3
\pages 373--389
\crossref{https://doi.org/10.1090/S1061-0022-07-00955-7}


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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, D. B. Karp, V. A. Shlyk, “Izbrannye zadachi geometricheskoi teorii funktsii i teorii potentsiala”, Dalnevost. matem. zhurn., 8:1 (2008), 46–95  mathnet  elib
    2. 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
    3. 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
    4. 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
    5. Karp D., Prilepkina E., “Reduced modulus with free boundary and its applications”, Ann. Acad. Sci. Fenn. Math., 34:2 (2009), 353–378  mathscinet  zmath  isi  elib
    6. 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
    7. V. V. Goryainov, “Holomorphic Mappings of a Strip into Itself with Bounded Distortion at Infinity”, Proc. Steklov Inst. Math., 298 (2017), 94–103  mathnet  crossref  crossref  isi  elib
  • Алгебра и анализ St. Petersburg Mathematical Journal
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