6 problems

Let $G$ and $H$ be simply connected nilpotent Lie groups. Two groups are quasiisometric when their underlying metric spaces are quasi-isometric. Quasiisometric rigidity conjecture.…

Let $X$ be a higher-rank symmetric space, and let $G$ be a finitely generated group quasiisometric to $X$. Margulis's conjecture. Every quasiisometry of $X$ should lie at bounded d…

Eskin–Fisher–Whyte's conjecture. The class of virtually polycyclic groups should be quasiisometrically complete within finitely generated groups.

Let $G$ and $H$ be completely solvable Lie groups, meaning closed subgroups of the upper triangular real matrix group. They are quasiisometric if their metric spaces are quasiisome…

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…