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An extremal problem on non-overlapping domains containing ellipse points
Ya. V. Zabolotnii, I. V. Denega Department of complex analysis and potential theory,
Institute of mathematics of the National Academy of Sciences of Ukraine,
3 Tereschenkivska St,
01024 Kyiv, Ukraine
Abstract:
An extremal problem of geometric function theory of a complex variable for the maximum
of products of the inner radii on a system of $n$ mutually non-overlapping multiply connected domains
$B_k$ containing the points $a_k$, $k=\overline{1,n}$, located on an arbitrary ellipse $\frac{x^2}{d^2}+\frac{y^2}{t^2}=1$ for which $d^2-t^2=1$,
is solved.
Keywords and phrases:
inner radius of the domain, mutually non-overlapping domains, the Green function, quadratic differential, the Goluzin theorem.
Received: 01.06.2020
Citation:
Ya. V. Zabolotnii, I. V. Denega, “An extremal problem on non-overlapping domains containing ellipse points”, Eurasian Math. J., 12:4 (2021), 82–91
Linking options:
https://www.mathnet.ru/eng/emj424 https://www.mathnet.ru/eng/emj/v12/i4/p82
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Statistics & downloads: |
Abstract page: | 69 | Full-text PDF : | 28 | References: | 8 |
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