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The problem of V. N. Dubinin for symmetric multiconnected domains. (English. Ukrainian original) Zbl 1469.30043

Ukr. Math. J. 72, No. 11, 1733-1741 (2021); translation from Ukr. Mat. Zh. 72, No. 11, 1502-1509 (2020).
Summary: We consider a quite general problem from the geometric theory of functions, namely, the problem of finding the maximal value of the product of inner radii of \(n\) nonoverlapping domains that contain points of the unit circle and are symmetric with respect to this circle and the \(\gamma\) power of the inner radius of a domain containing the origin. The posed problem is solved for \(n \geq 20\) and \(1<\gamma \le n^{\frac{2}{3}-q(n)}\).

MSC:

30C55 General theory of univalent and multivalent functions of one complex variable
30C35 General theory of conformal mappings
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References:

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