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Ufa Mathematical Journal, 2017, Volume 9, Issue 2, Pages 55–61
DOI: https://doi.org/10.13108/2017-9-2-55 (Mi ufa375) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Lower bounds for the area of the image of a circle

B. A. Klishchuk, R. R. Salimov

Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev
English version PDF (349 kB) Citations (15)
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DOI: https://doi.org/10.13108/2017-9-2-55
Abstract: In the work we consider $Q$-homeomorphisms w.r.t $p$-modulus on the complex plane as $p>2$. We obtain a lower bound for the area of the image of a circle under such mappings. We solve the extremal problem on minimizing the functional of the area of the image of a circle.
Keywords: $p$-modulus of a family of curves, $p$-capacity of condenser, quasiconformal mappings, $Q$-homeomorphisms w.r.t. $p$-modulus.
Received: 16.06.2016
Russian version:
Ufimskii Matematicheskii Zhurnal, 2017, Volume 9, Issue 2, Pages 56–62
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: 30С65
Language: English
Original paper language: Russian
Citation: B. A. Klishchuk, R. R. Salimov, “Lower bounds for the area of the image of a circle”, Ufimsk. Mat. Zh., 9:2 (2017), 56–62; Ufa Math. J., 9:2 (2017), 55–61
Citation in format AMSBIB
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\pages 56--62
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Уфимский математический журнал
    Statistics & downloads:
    Abstract page:355
    Russian version PDF:137
    English version PDF:9
    References:62
     
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