Some extremal problems on the Riemannian sphere - Denega, I.V.; Zabolotnyi, Ya.V. (Carpathian Mathematical Publications, 2024)
In the paper, the open problem on maximum of the product of inner radii of n domains in the case, when points and domains belong to the unit disk, is investigated. This problem is solved only for n=2 and n=3. No other results are known at present. We obtain the result for all n 2. Also, we propose an approach that allows to establish evolutionary inequalities for the products of the inner radii of mutually non-overlapping domains.