Twisted Patterson-Sullivan measures and applications to amenability and coverings

Rémi Coulon, Rhiannon Dougall, Barbara Schapira +1

Let ${\Gamma }^{\prime }<\Gamma$ be two discrete groups acting properly by isometries on a Gromov-hyperbolic space $X$. We prove that their critical exponents coincide if and only if ${\Gamma }^{\prime }$ is co-amenable…