We show that for every non-elementary hyperbolic group the Bowen–Margulis current associated with a strongly hyperbolic metric forms a unique group-invariant Radon measure class of maximal Hausdorff dimension on the boundary square. Applications include a characterization of roughly similar hyperbolic metrics via mean distortion.

中文翻译：

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双曲群的拓扑流

我们表明，对于每个非初等双曲群，与强双曲度量相关的 Bowen-Margulis 电流在边界正方形上形成一个唯一的群不变 Radon 测量类，该类具有最大 Hausdorff 维数。应用包括通过平均失真对大致相似的双曲线度量进行表征。