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Uniformly Lipschitz Hyperbolic Group Actions on ℓp
Abstract
Let Γ be a finitely generated hyperbolic group, and let Q denote the conformal dimension of its Gromov boundary ∂Γ. We prove that for every p < Q/(Q−1), the group Γ admits a proper uniformly Lipschitz affine action on ℓp with compression exponent 1/p. The ℓp-space hosting the action is designed from a Markov chain on a specialized hyperbolic filling of ∂Γ.
Related
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BibTeX
@misc{gartland2026uniformly,
title = {{Uniformly Lipschitz Hyperbolic Group Actions on $\ell^p$}},
author = {Chris Gartland and Tianyi Zheng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30583},
eprint = {2609.30583},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30583},
}
RIS
TY - UNPB
TI - Uniformly Lipschitz Hyperbolic Group Actions on ℓ^p
AU - Chris Gartland
AU - Tianyi Zheng
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30583
UR - https://arxiv.org/abs/2609.30583
AB - Let Γ be a finitely generated hyperbolic group, and let Q denote the conformal dimension of its Gromov boundary ∂Γ. We prove that for every p < Q/(Q−1), the group Γ admits a proper uniformly Lipschitz affine action on ℓ^p with compression exponent 1/p. The ℓ^p-space hosting the action is designed from a Markov chain on a specialized hyperbolic filling of ∂Γ.
ER -