Quasisymmetric universality, quasi-isometric classification and topological rigidity of Kleinian groups

Peter Haïssinsky; Yusheng Luo

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arXiv · 2608.12287

Quasisymmetric universality, quasi-isometric classification and topological rigidity of Kleinian groups

Peter Haïssinsky·Yusheng Luo

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Abstract

We study the quasisymmetric classification of limit sets of Kleinian groups and obtain a characterization of those geometrically finite limit sets that are quasisymmetrically universal. This allows us to obtain a quasi-isometric classification of finitely generated Kleinian groups. We also obtain a classification of virtually topologically rigid geometrically finite Kleinian groups.

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Peter Haïssinsky, Yusheng Luo. 2026-08-12. Quasisymmetric universality, quasi-isometric classification and topological rigidity of Kleinian groups. https://arxiv.org/abs/2608.12287

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