Inequalities for inner radii of symmetric disjoint domains - Bakhtin, A. K.; Vyhovs'ka, L.V.; Denega, I. V. (Ukrains’kyi Matematychnyi Zhurnal, 2018)
We study the following problem: Let a_0 = 0, | a_1| = ... = | a_n| = 1, a_k B_k C, where B_0, ... ,B_n are disjoint domains, and B_1, ... ,B_n are symmetric about the unit circle. It is necessary to find the exact upper bound for r^γ (B_0, 0) ^n_k=1 r(B_k, a_k), where r(B_k, a_k) is the inner radius of Bk with respect to a_k. For γ = 1 and n ≥ 2, the problem was solved by L. V. Kovalev. We solve this problem for γ (0, γ_n], γ_n = 0,38 n^2, and n ≥ 2 under the additional assumption imposed on the angles between the neighboring line segments [0, a_k].