Extremal problems on the generalized (n, d)-equiangular system of points

Abstract

The paper of Lavrent’ev [1] was the beginning of geometrical theory of functions of the complex variable. He solved a problem on the product of conformal radiuses of two non-overlapping domains. In many papers (see [2] – [13]) the Lavrent’ev’s result are generalized. In this paper are obtained the new results of this direction.

Keywords

• inner radius of domain
• quadratic differential
• piecewise-separating transformation
• the green function
• radial systems of points
• logarithmic capacity
• variational formula
• primary 30c70, 30c75