ABOUT ONE PROBLEM ON EXTREMAL DECOMPOSITION

Abstract

In the paper, we consider an open problem of finding the maximum of product of inner radii of mutually non-overlapping domains with respect to the points of the unit circle on a certain positive degree 𝛾 of the inner radius of the domain with respect to the origin, moreover, the domain containing origin does not intersect with other domains.

Keywords

• inner radius of the domain
• mutually non-overlapping domains
• the green function
• quadratic differential
• the dubinin problem