Modulus estimates of semirings with applications to boundary extension problems

TL;DR

This paper extends previous work on boundary extension problems by analyzing modulus estimates of semirings and their applications to boundary correspondence issues under a broader class of mappings.

Contribution

It generalizes earlier results on ring domains to semirings, providing new modulus estimates and applications to boundary extension problems for more general mappings.

Findings

Established new modulus estimates for semirings.

Extended boundary extension results to a larger class of mappings.

Applied these results to boundary correspondence problems.

Abstract

In our previous paper [GSV2020], we proved that the complementary components of a ring domain in $\mathbb{R}^n$ with large enough modulus may be separated by an annular ring domain and applied this result to boundary correspondence problems under quasiconformal mappings. In the present paper, we continue this work and investigate boundary extension problems for a larger class of mappings.