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arXiv · 2212.12837

Groups that (do not) act isometrically on hyperbolic spaces

Yanlong Hao
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Abstract

In this paper, we show that if a group acts isometrically on a good hyperbolic space of finite volume entropy through a non-elementary action, then it admits an affine action on some $L^p$ -space with an unbounded orbit for sufficiently large $p$. As an application, we prove that any isometric action of a group with the fixed point property $F_\infty$ on a good hyperbolic space must have a bounded orbit.

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Yanlong Hao. 2022-12-25. Groups that (do not) act isometrically on hyperbolic spaces. https://arxiv.org/abs/2212.12837

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