ESTIMATE OF THE MAXIMUM PRODUCT OF INNER RADII OF NON-OVERLAPPING DOMAINS

Abstract

In this paper, the upper estimate for the maximum of the products of inner radii of mutually non-overlapping domains is obtained for any 𝑛-radial system of points on the complex plane at all possible values of some parameter 𝛾. The conditions under which the structure of points is not important in the proved results are established.

Keywords

• inner radius of domain
• non-overlapping domains
• the green function
• transfinite diameter
• theorem on minimizing of the area
• the cauchy inequality