Extremal decomposition problems for p-harmonic Robin radius

The theorems on the extremal decomposition of plane domains concerning to the products of Robin's radii are extended to the case of domains in Euclidean space. In some cases, the classical non-overlapping condition is weakened. The proofs are based on the moduli technique for families of curves and dissymmetrization.

Problem on extremal decomposition of the complex plane with free poles

We consider the well-known problem of the geometric theory of functions of a complex variable on non-overlapping domains with free poles on radial systems. The main results of the present work strengthen and generalize several known results for this problem.

Extremal decomposition of the complex plane with free poles. II

Problems on extremal decomposition of the complex plane with free poles located on an (n,m)-ray system of points are studied. A method that allowed us to obtain new upper bounds for the maximum of the products of the inner radii of mutually non-overlapping domains is proposed.

Estimates of the inner radii of non-overlapping domains

Some extremal problems of the geometric theory of functions of a complex variable related to the estimates of functionals defined on systems of non-overlapping domains are considered. Till now, many such problems have not been solved, though some partial solutions are available. In the paper, the improved method is proposed for solving the problems on extremal decomposition of the complex plane. The main results generalize and strengthen some known results in the theory of non-overlapping domains with free poles to the case of an arbitrary arrangement of systems of points on the complex plane.