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arXiv · 2509.20532

A notion of quasiconvex subgroups in acylindrically hyperbolic groups

Ping Wan
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Abstract

In this paper, we present a notion of quasiconvexity in the setting of finitely-generated groups with hyperbolically embedded subgroups. Our main result shows that this notion yields uniform quasiconvex constants in the setting of coned-off cusped spaces. We also prove that this notion of quasiconvexity is preserved under sufficiently long Dehn filling. As an application, we generalize a theorem of Groves-Manning on groups acting on $\operatorname{CAT}(0)$ cube complexes.

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Ping Wan. 2025-09-24. A notion of quasiconvex subgroups in acylindrically hyperbolic groups. https://arxiv.org/abs/2509.20532

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