On asymptotically symmetric embeddings and conformal maps

Ylli Andoni; Shanshuang Yang

doi:10.1112/mtk.70112

June 23, 2026MathematikaOpen Access

On asymptotically symmetric embeddings and conformal maps

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Key Points

Investigate the conditions under which conformal maps from the unit disk exhibit asymptotic symmetry.
Analyzed conformal maps of the unit disk to a bounded Jordan domain.
Explored the geometric properties of symmetric quasicircles.
Developed theoretical proofs to establish symmetry-related conditions.
Conformal maps are shown to be asymptotically symmetric if and only if bounded by a symmetric quasicircle.

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Implication

Demonstrates the relationship between conformal maps and symmetric quasicircles in bounded domains, indicating implications for geometric function theory.

Abstract

This paper is devoted to the study of conformal maps of the unit disk in the plane onto a bounded Jordan domain . The main aim is to show that such a map is asymptotically symmetric if and only if is bounded by a symmetric quasicircle.

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Andoni et al. (2026) studied this question.

synapsesocial.com/papers/6a3e15e7030ad1a9b308fe54 https://doi.org/10.1112/mtk.70112

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On asymptotically symmetric embeddings and conformal maps

Key Points

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Implication

Abstract

Discussion

Cite This Study

On asymptotically symmetric embeddings and conformal maps

Key Points

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Implication

Abstract

Discussion

Cite This Study

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