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.
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
\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}
Linking options:
https://www.mathnet.ru/eng/znsl6430
https://www.mathnet.ru/eng/znsl/v456/p160
This publication is cited in the following 6 articles:
Ruslan Salimov, Bogdan Klishchuk, Trends in Mathematics, New Tools in Mathematical Analysis and Applications, 2025, 89
Mariia V. Stefanchuk, “On exponential asymptotics of ring Q-homeomorphisms at infinity”, J Math Sci, 282:1 (2024), 83
Mariia Volodymyrivna Stefanchuk, “On exponential asymptotics of one class of homeomorphisms at a point of the complex plane”, PIGC, 17:2 (2024), 158
Mariia V. Stefanchuk, “On exponential asymptotics of ring Q-homeomorphisms at infinity”, UMB, 21:1 (2024), 107
M.V. Stefanchuk, “On asymptotic behavior at infinity of lower Q-homeomorphisms with respect to p-modulus on the complex plane”, Proc. IAMM NASU, 38 (2024), 103
Bogdan Klishchuk, Ruslan Salimov, Mariia Stefanchuk, “On the asymptotic behavior at infinity of one mapping class”, PIGC, 16:1 (2023), 50
Citation in format AMSBIB
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