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Dal'nevost. Mat. Zh., 2013, Volume 13, Number 2, Pages 196–208 (Mi dvmg263)  

This article is cited in 2 scientific papers (total in 2 papers)

Generalized condensers and boundary distortion theorems for conformal mappings

V. N. Dubininab, V. Yu. Kima

a Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok
b Far Eastern Federal University, Vladivostok

Abstract: In this paper we prove some boundary distortion theorems for the univalent holomorphic functions in the unit disk by the potential theory. In particular, the discrete analogs of the classical statements on the behavior of the logarithmic capacity of the boundary sets under conformal mappings are established.

Key words: condensers, conformal capacity, meromorphic functions, univalent functions, boundary distortion, angular derivative

Full text: PDF file (154 kB)
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UDC: 517.54
MSC: Primary 30C85; Secondary 30C75
Received: 14.05.2013

Citation: V. N. Dubinin, V. Yu. Kim, “Generalized condensers and boundary distortion theorems for conformal mappings”, Dal'nevost. Mat. Zh., 13:2 (2013), 196–208

Citation in format AMSBIB
\Bibitem{DubKim13}
\by V.~N.~Dubinin, V.~Yu.~Kim
\paper Generalized condensers and boundary distortion theorems for conformal mappings
\jour Dal'nevost. Mat. Zh.
\yr 2013
\vol 13
\issue 2
\pages 196--208
\mathnet{http://mi.mathnet.ru/dvmg263}


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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, “On the reduced modulus of the complex sphere”, Siberian Math. J., 55:5 (2014), 882–892  mathnet  crossref  mathscinet  isi
    2. 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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