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arXiv · 2510.12281

Analytic Characterization of $t$-Quasicircles and Conformal Mappings onto $t$-Quasidisks

Xin Wei
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Abstract

In this paper, we introduce a new class of mappings, termed $(\rho,t)$-quasisymmetric mappings, which generalizes the classical concept of quasisymmetric mappings. Using this broader class of mappings, we provide an analytic characterization of $t$-quasicircles. This result can be viewed as a $t$-quasisymmetric analogue of a classical theorem by Tukia and V\"ais\"al\"a \cite{TV}. Furthermore, we study conformal mappings from the unit disk $\mathbb{D}$ onto $t$-quasidisks and show that their boundary values are "almost`` $(\rho,t^2)$-quasisymmetric. This result extends the Quasicircle Theorem to the case of $t$-quasicircles.

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Xin Wei. 2025-10-14. Analytic Characterization of $t$-Quasicircles and Conformal Mappings onto $t$-Quasidisks. https://arxiv.org/abs/2510.12281

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