Mikołaj Frączyk

On some aspects of discrete groups acting ergodically on the boundary

We show that if $G$ is a real semisimple Lie group and $\Gamma<G$ is a discrete subgroup with slow growth, in the sense that its growth indicator function is smaller than $\rho$, then $\Gamma$ acts totally dissipatively on the Furstenberg boundary of $G$. Moreover, for $G= SO(n,2)$ and $n\geq 3$, we construct infinite-...