arXiv subjects

Mikhail Borovikov

Publications and source records attributed to Mikhail Borovikov.

2 recordsLinked to original sources

arXiv2025

On Koebe radius and coefficients estimate for univalent harmonic mappings

The problem on estimate of the Koebe radius for univalent harmonic mappings of the unit disk $\mathbb D=\{z\in\mathbb C : |z|<1\}$ is considered. For a subclass of harmonic mappings with the standard normalization and a certain growth estimate for analytic dilatation, we provide new estimate for the Koebe radius. New estimate for Taylor coefficients of the holomorphic part of a function from the subclass under consideration is obtained as a corollary.

math.CV↗

arXiv2025

On $L$-special domains with algebraic boundaries

The concept of $L$-special domain appeared in the early 2000s. This analytical characteristic of domains in the complex plane is related to the problem on uniform approximation of functions on Carathéodory compacts in $\mathbb{R}^2$ by polynomial solutions of homogeneous second-order elliptic partial differential equations $Lu=0$ with constant complex coefficients. In this paper, new properties and examples of $L$-special domains with algebraic boundaries are obtained.

math.CV↗