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Dal'nevost. Mat. Zh., 2005, Volume 6, Number 1-2, Pages 39–56 (Mi dvmg197)  

This article is cited in 8 scientific papers (total in 8 papers)

On the preservation of generalized reduced modulus under some geometric transformations of domains in the plane

V. N. Dubinin, E. G. Prilepkina

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

Abstract: We study necessary and sufficient conditions for the preservation of the generalized reduced modulus under the extension of domain or a part of its boundary. Also, we give such conditions for polarization and dissymmetrization. As applications, the descriptions of extremal configurations in the known inequalities for the inner radii, the Green functions and the Robin functions are obtained. Some of our results supplement the known boundary distortion theorems for univalent regular functions.

Key words: capacity of condenser, reduced modulus, polarization, dissymmetrization, Green function, Robin function, regular functions.

Full text: PDF file (327 kB)
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Document Type: Article
UDC: 517.54, 517.956
MSC: Primary 31A15; Secondary 30C85
Received: 04.07.2005

Citation: V. N. Dubinin, E. G. Prilepkina, “On the preservation of generalized reduced modulus under some geometric transformations of domains in the plane”, Dal'nevost. Mat. Zh., 6:1-2 (2005), 39–56

Citation in format AMSBIB
\Bibitem{DubPri05}
\by V.~N.~Dubinin, E.~G.~Prilepkina
\paper On the preservation of generalized reduced modulus under some geometric transformations of domains in the plane
\jour Dal'nevost. Mat. Zh.
\yr 2005
\vol 6
\issue 1-2
\pages 39--56
\mathnet{http://mi.mathnet.ru/dvmg197}
\elib{http://elibrary.ru/item.asp?id=15484721}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. 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
    3. E. G. Prilepkina, “Teoremy iskazheniya dlya odnolistnykh funktsii v mnogosvyaznykh oblastyakh”, Dalnevost. matem. zhurn., 9:1-2 (2009), 140–149  mathnet
    4. 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
    5. E. G. Prilepkina, “On composition principles for reduced moduli”, Siberian Math. J., 52:6 (2011), 1079–1091  mathnet  crossref  mathscinet  isi
    6. E. G. Prilepkina, “Transfinite diameter with respect to Neumann function”, J. Math. Sci. (N. Y.), 200:5 (2014), 605–613  mathnet  crossref
    7. V. N. Dubinin, “On the reduced modulus of the complex sphere”, Siberian Math. J., 55:5 (2014), 882–892  mathnet  crossref  mathscinet  isi
    8. E. G. Prilepkina, “On quadratic forms generated by the Neumann functions”, J. Math. Sci. (N. Y.), 207:6 (2015), 909–922  mathnet  crossref
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