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Zapiski Nauchnykh Seminarov POMI, 2017, Volume 456, Pages 160–171 (Mi znsl6430)  
This article is cited in 3 scientific papers (total in 3 papers)

A extremal problem for the areas of images of disks

R. R. Salimov, B. A. Klishchuk

Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev, Ukraine
Full-text PDF (211 kB) Citations (3)
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Abstract: We study metric properties of the ring $Q$-homeomorphisms with respect to the $p$-modulus, $p>2$, in the complex plane and establish lower bounds for the areas of disks. The extremal problem concerning minimization of the area functional is also solved.
Key words and phrases: ring $Q$-homeomorphism, $p$-modulus of families of curves, capacitor, $p$-capacitance of a capacitor, area functional.
Received: 25.05.2017
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 234, Issue 3, Pages 373–380
DOI: https://doi.org/10.1007/s10958-018-4015-6
Document Type: Article
UDC: 517.9
Language: Russian
Citation: R. R. Salimov, B. A. Klishchuk, “A extremal problem for the areas of images of disks”, Investigations on linear operators and function theory. Part 45, Zap. Nauchn. Sem. POMI, 456, POMI, St. Petersburg, 2017, 160–171; J. Math. Sci. (N. Y.), 234:3 (2018), 373–380
Citation in format AMSBIB
\Bibitem{SalKli17}
\by R.~R.~Salimov, B.~A.~Klishchuk
\paper A extremal problem for the areas of images of disks
\inbook Investigations on linear operators and function theory. Part~45
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 456
\pages 160--171
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6430}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 234
\issue 3
\pages 373--380
\crossref{https://doi.org/10.1007/s10958-018-4015-6}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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