The radius of injectivity of local ring $Q$-homeomorphisms

TL;DR

This paper investigates the injectivity radius of local Q-homeomorphisms, establishing sharp conditions for their injectivity near a point, extending classical results on quasiconformal mappings.

Contribution

It extends the theorem on radius injectivity to a broader class of mappings with unbounded quasiconformal characteristics, providing new sharp conditions for local injectivity.

Findings

Established sharp injectivity conditions for local Q-homeomorphisms.

Extended classical quasiconformal mapping theorems to mappings with unbounded characteristics.

Proved the analog of the radius injectivity theorem for a new class of mappings.

Abstract

The paper is devoted to the study of mappings with non--bounded characteristics of quasiconformality. The analog of the theorem about radius injectivity of locally quasiconformal mappings was proved for some class of mappings. There are found sharp conditions under which the so called local $Q$--homeomorphisms are injective in some neighborhood of a fixed point.