3 problems

Ballmann's higher rank rigidity conjecture. Any Hadamard space of rank at least two with a geometric group action admits an affine map which is not a dilation.

Let $n \geq 3$ and let $H$ be the diagonal subgroup acting on $\operatorname{PGL}_n(\mathbb{Z}) \backslash \operatorname{PGL}_n(\mathbb{R})$. Finiteness conjecture for periodic orb…

Let $n \geq 3$, let $G \cong \operatorname{PGL}_n(\mathbb{R})$, and let $\Gamma < G$ be a lattice as in examples (L-1) or (L-2) of the source. Let $H$ be the relevant diagonal subg…