  We construct 4-dimensional CAT(0) groups containing finitely presented
subgroups whose Dehn functions are $\exp^{(n)}(x^m)$ for integers $n, m \geq 1$
and 6-dimensional CAT(0) groups containing finitely presented subgroups whose
Dehn functions are $\exp^{(n)}(x^\alpha)$ for integers $n \geq 1$ and $\alpha$
dense in $[1,\infty)$. This significantly expands the known geometric behavior
of subgroups of CAT(0) groups.
