Inequalities for the inner radii of nonorevlapping domains
UDC 517.54 We consider the problem of maximum of the functional r^γ(B_0,0)_k=1^n r(B_k,a_k), where B_0,…,B_n, n≥ 2, are pairwise disjoint domains in C , a_0=0, |a_k|=1, k=1,n, and γ(0, n] (r(B,a) is the inner radius of the domain BC with respect to a). Show that it attains its maximum at a configuration of domains B_k and points a_k possessing rotational n-symmetry. This problem was solved by Dubinin for γ=1 and by Kuz’mina for 0, number=7, journal=Ukrains’kyi Matematychnyi Zhurnal, author=Bakhtin, A. K. and Denega, I. V., year=2019, month=Jul., pages=996–1002