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Algebra i Analiz, 2006, Volume 18, Issue 3, Pages 39–62 (Mi aa73)  
This article is cited in 8 scientific papers (total in 8 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
Full-text PDF (257 kB) Citations (8)
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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.
Received: 22.02.2006
English version:
St. Petersburg Mathematical Journal, 2007, Volume 18, Issue 3, Pages 373–389
DOI: https://doi.org/10.1090/S1061-0022-07-00955-7
Bibliographic databases:
Document Type: Article
MSC: 30C70, 30C85
Language: Russian
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
\Bibitem{DubPri06}
\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://mathscinet.ams.org/mathscinet-getitem?mr=2255850}
\zmath{https://zbmath.org/?q=an:1146.30011}
\elib{https://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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  • https://www.mathnet.ru/eng/aa73
  • https://www.mathnet.ru/eng/aa/v18/i3/p39
    • This publication is cited in the following 8 articles:
    1. V. N. Dubinin, “Variational formulae for conformal capacity”, Sb. Math., 215:1 (2024), 90–100  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. 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
    3. 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
    4. 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
    5. 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
    6. 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
    7. 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
    8. 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
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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