Topological flows for hyperbolic groups
arXiv:1912.03808 · doi:10.1017/etds.2020.101
Abstract
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.
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