2 problems

Let $S$ be a Heintze group, and let $\phi$ be a self-quasiisometry of $S$. The Gromov boundary of $S$ is the boundary on which $\phi$ induces an extension. Assume that $S$ is not o…

Let $S$) be a Heintze group that is not among the special-type subgroups of $\operatorname{SO}(n,1)$ or $\operatorname{SU}(n,1)$ for any $n\geqslant 2$. Equip $S$ with any left-inv…