2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/216170We establish the existence, finiteness, and uniqueness up to scaling of various isoperimetric profiles of a group, in all dimensions. We also show that these profiles all coincide in dimensions 4 and higher; in particular, the nth Dehn function is equal to FV^{n+1} for n at least 3. Even for dimension 3, there is significant overlap. When a group has decidable word problem, this has mild consequences for the growth rates of its profiles. We also establish a metric analogue for highly connected Riemannian manifolds.10 pagesGroup TheoryGeometric Topology20F65 (primary), 53C23 (secondary)text