9 problems

A purely real Heintze group is a negatively curved homogeneous Lie group of the form $N\rtimes_\alpha\mathbb{R}$, where $N$ is a simply connected nilpotent Lie group and the deriva…

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…

A purely real Heintze group is a Heintze group whose defining derivation has only real eigenvalues. Two groups are quasi-isometric if they admit a quasi-isometry between suitable w…

A Heintze group is a solvable simply connected Lie group admitting a left-invariant Riemannian metric with negative sectional curvature. Two Lie groups can be made isometric if the…

A purely real Heintze group is a Heintze group $N\rtimes_\alpha\mathbb{R}$ whose defining derivation $\alpha$ has only real eigenvalues. Quasi-isometric rigidity conjecture. Two pu…

A purely real Heintze group is a solvable Lie group of the form $N\rtimes_\alpha \mathbb{R}$, where $N$ is a connected, simply connected nilpotent Lie group and $\alpha$ is a deriv…

Let $H$ be a purely real Heintze group of dimension at least $2$, and let $\partial H$ denote its boundary. Let $\omega$ be the point of $\partial H$ fixed by $H$. Pointed sphere c…

Let $H=N\rtimes\mathbf{R}$ be a purely real Heintze group of dimension at least $2$: a simply connected Lie group in which $\mathbf{R}$ contracts the non-trivial simply connected n…