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.
\Bibitem{KliSal17}
\by B.~A.~Klishchuk, R.~R.~Salimov
\paper Lower bounds for the area of the image of a circle
\jour Ufa Math. J.
\yr 2017
\vol 9
\issue 2
\pages 55--61
\mathnet{http://mi.mathnet.ru/eng/ufa375}
\crossref{https://doi.org/10.13108/2017-9-2-55}
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\elib{https://elibrary.ru/item.asp?id=29419144}
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Linking options:
https://www.mathnet.ru/eng/ufa375
https://doi.org/10.13108/2017-9-2-55
https://www.mathnet.ru/eng/ufa/v9/i2/p56
This publication is cited in the following 17 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
R. R. Salimov, V. A. Klishchuk, “On the Behavior of One Class of Homeomorphisms at Infinity”, Ukr Math J, 74:10 (2023), 1617
Igor Petkov, Ruslan Salimov, Mariia Stefanchuk, “On the distortion of the disk image diameter”, UMB, 20:2 (2023), 219
R. Salimov, L. Vyhivska, B. Klishchuk, “Pro spotvorennya transfіnіtnogo dіametra obrazu kruga”, Ukr. Mat. Zhurn., 75:2 (2023), 207
Bogdan A. Klishchuk, “On Power-Law Behavior of Some Mapping Class at Infinity”, J Math Sci, 268:2 (2022), 192
E. Deniz, S. Kanas, H. Orhan, “Univalence criteria and quasiconformal extension of a general integral operator”, Ukr. Mat. Zhurn., 74:1 (2022), 24
Ruslan Salimov, Bogdan Klishchuk, Trends in Mathematics, Current Trends in Analysis, its Applications and Computation, 2022, 173
R. R. Salimov, B. A. Klishchuk, “Pro povedіnku odnogo klasu gomeomorfіzmіv na neskіnchennostі”, Ukr. Mat. Zhurn., 74:10 (2022), 1416
Aleksandr K. Bakhtin, Iryna V. Denega, “Generalized M.A. Lavrentiev's inequality”, J Math Sci, 262:2 (2022), 138
Aleksandr Bakhtin, Iryna Denega, “Generalized M.A. Lavrentiev's inequality”, UMB, 19:1 (2022), 14
E. Deniz, S. Kanas, H. Orhan, “Univalence Criteria and Quasiconformal Extension of a General Integral Operator”, Ukr Math J, 74:1 (2022), 27
Cristea M., “on Poleckii-Type Modular Inequalities”, Complex Var. Elliptic Equ., 66:11 (2021), 1818–1838
A. K. Bakhtin, “A problem of extreme decomposition of the complex plane with free poles”, Ukr. Math. J., 71:10 (2020), 1485–1509
Iryna Denega, “Estimation of the products of the inner radii of domains with an additional symmetry condition”, Proc. IAMM NASU, 33 (2019), 83
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