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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2510.12281 |
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| _version_ | 1866908716697124864 |
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| author | Wei, Xin |
| author_facet | Wei, Xin |
| contents | In this paper, we introduce a new class of mappings, termed $(ρ,t)$-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 Väisälä \cite{TV}. Furthermore, we study conformal mappings from the unit disk $\mathbb{D}$ onto $t$-quasidisks and show that their boundary values are "almost`` $(ρ,t^2)$-quasisymmetric. This result extends the Quasicircle Theorem to the case of $t$-quasicircles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12281 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analytic Characterization of $t$-Quasicircles and Conformal Mappings onto $t$-Quasidisks Wei, Xin Complex Variables In this paper, we introduce a new class of mappings, termed $(ρ,t)$-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 Väisälä \cite{TV}. Furthermore, we study conformal mappings from the unit disk $\mathbb{D}$ onto $t$-quasidisks and show that their boundary values are "almost`` $(ρ,t^2)$-quasisymmetric. This result extends the Quasicircle Theorem to the case of $t$-quasicircles. |
| title | Analytic Characterization of $t$-Quasicircles and Conformal Mappings onto $t$-Quasidisks |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2510.12281 |