Year: 2026
Type: preprint
Abstract: Let $Γ$ be a finitely generated hyperbolic group, and let $Q$ denote the conformal dimension of its Gromov boundary $\partialΓ$. We prove that for every $p < \frac{Q}{Q-1}$, the group $Γ$ admits a proper uniformly Lipschitz affine action on $\ell^p$ with compression exponent $1/p$. The $\ell^p$-space hosting the action is designed from a Markov chain on a specialized hyperbolic filling of $\partialΓ$.
Source: arXiv (Cornell University)
Authors: Gartland, Chris, Zheng, Tianyi
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7214617929