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 γ power of the inner radius of a domain containing the origin. The posed problem is solved for n ≥ 20 and \( 1<\gamma \le {n}^{\frac{2}{3}-q(n)} \).

中文翻译：

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对称多连通域的 VN Dubinin 问题

我们从函数的几何理论中考虑一个相当普遍的问题，即找到包含单位圆的点并关于该圆和γ对称的n 个非重叠域的内半径乘积的最大值的问题包含原点的域的内半径的幂。对于n ≥ 20 和\( 1<\gamma \le {n}^{\frac{2}{3}-q(n)} \)解决了所提出的问题。