On asymptotics of ring $Q$-homeomorphisms with respect to $p$-modulus near the origin

TL;DR

This paper investigates the behavior of ring $Q$-homeomorphisms near the origin, establishing lower bounds for their distortion and demonstrating Hölder continuity of their inverses through sharp estimates and examples.

Contribution

It provides new lower bounds for the asymptotic distortion of ring $Q$-homeomorphisms with respect to $p$-modulus near the origin, including sharpness analysis.

Findings

Established lower bounds for the limsups of distance distortions

Proved Hölder continuity of inverses near the origin

Provided examples illustrating the sharpness of estimates

Abstract

We consider the class of ring $Q$-homeomorphisms with respect to $p$-modulus in $\mathbb{R}^{n}$ with $p > n$, and obtain lower bounds for limsups of the distance distortions under such mappings. These estimates can be treated as H\"{o}lder's continuity of the inverses near the origin. The sharpness is illustrated by example