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Ufimsk. Mat. Zh., 2017, Volume 9, Issue 2, Pages 56–62 (Mi ufa375)  

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

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.

Full text: PDF file (386 kB)
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English version:
Ufa Mathematical Journal, 2017, 9:2, 55–61 (PDF, 349 kB); https://doi.org/10.13108/2017-9-2-55

Bibliographic databases:

UDC: 517.5
MSC: 30С65
Received: 16.06.2016

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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