Some extremal problems on the Riemannian sphere
Year: 2024
Type: article
Abstract: In the paper, the open problem of the maximum product of the inner radii of $n$ domains in the case, when points and domains belong to the unit circle, 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 $n \geqslant 2$. Also, we propose an approach that allows to establish evolutionary inequalities for the products of the inner radii of mutually non-overlapping domains.
Authors: I.V. Denega, Ya.V. Zabolotnyi
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4405917570