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arXiv · 2402.12709

On quasiconformal non-equivalence of gasket Julia sets and limit sets

Yusheng Luo·Yongquan Zhang
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Abstract

This paper studies quasiconformal non-equivalence of Julia sets and limit sets. We proved that any Julia set is quasiconformally different from the Apollonian gasket. We also proved that any Julia set of a quadratic rational map is quasiconformally different from the gasket limit set of a geometrically finite Kleinian group.

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Yusheng Luo, Yongquan Zhang. 2024-02-20. On quasiconformal non-equivalence of gasket Julia sets and limit sets. https://doi.org/10.1017/etds.2025.10191

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