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arXiv · 2309.15452

On invariance of John domains under quasisymmetric mappings

Vasudevarao Allu·Alan P Jose
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Abstract

In this paper, we prove that if a homeomorphism is quasisymmetric relative to the boundary of the domain then it maps a length John domain to a diameter John domain. Moreover, we prove a necessary and sufficient condition for a diameter John domain to be length John and thereby prove that if $f:G\rightarrow G'$ is $(M, C)-$CQH map, where $G$ is a John domain, and the map extends to the boundary such that the extension is $\eta-$QS relative to $\delta G$ then $G'$ is a John domain. In addition, we characterize distance John domains using the weak minimizing property.

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Vasudevarao Allu, Alan P Jose. 2023-09-27. On invariance of John domains under quasisymmetric mappings. https://arxiv.org/abs/2309.15452

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