Superexponential Dehn functions inside CAT(0) groups

Abstract

We construct 4-dimensional CAT(0) groups containing finitely presented subgroups whose Dehn functions are exp (n) (x m ) for integers n, m ≥ 1 and 6-dimensional CAT(0) groups containing finitely presented subgroups whose Dehn functions are exp (n) (x α ) for integers n ≥ 1 and α dense in [1, ∞). This significantly expands the known geometric behavior of subgroups of CAT(0) groups.