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arXiv · 2604.13898

Hyperbolic spaces with geometric and geometrically finite quasi-actions are symmetric

Daniel Groves·Emily Stark·Genevieve S. Walsh·Kevin Whyte
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Abstract

We prove that if a proper metric space is quasi-isometric to a finitely generated group and to a space with a horoball over a finitely generated group, then that space is quasi-isometric to a rank-one symmetric space or the real line.

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Daniel Groves, Emily Stark, Genevieve S. Walsh, Kevin Whyte. 2026-04-15. Hyperbolic spaces with geometric and geometrically finite quasi-actions are symmetric. https://arxiv.org/abs/2604.13898

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