  We 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.
