2 problems

Let $X$ be a locally compact geodesically complete CAT(0) space with Tits diameter $\pi$, and suppose that $X$ supports a geometric group action $\Gamma\curvearrowright X$. If $X$…

Let $X$ be a proper CAT(0) space with a proper cocompact action of a discrete group $\Gamma$. A flat $F\subset X$ is $\Gamma$-periodic if some subgroup $\Gamma_0\leq\Gamma$ preserv…