3 problems

Let $G$ act properly and cocompactly by isometries on a CAT(0) space $X$, and let $d$ be a positive integer. Flat Closing Conjecture. The space $X$ contains a $d$-dimensional flat…

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 and let $\Gamma$ be a discrete group acting properly and cocompactly by isometries on $X$. A $d$-dimensional flat in $X$ is an isometrically embedd…