On removable singularities of one class of mappings satisfying moduli ine\-qua\-li\-ti\-es

TL;DR

This paper investigates the local behavior of Q-mappings, including quasiconformal and bounded distortion mappings, demonstrating conditions under which they have removable isolated singularities based on their growth relative to the radius.

Contribution

It establishes new criteria for removable singularities of Q-mappings related to their growth, extending understanding of their local behavior.

Findings

Q-mappings have removable isolated singularities under certain growth conditions.

The study includes quasiconformal mappings and mappings with bounded distortion.

Growth constraints determine the removability of singularities.

Abstract

A paper is devoted to study of local behavior of so-called $Q$-mappings including qua\-si\-con\-for\-mal mappings and mappings with bounded distortion. It is showed that, such mappings have removable isolated singularities whenever the grow of the mappings is note more than some function of a radius of a ball.