We prove that on a Riemannian manifold, a smooth differential form has a
primitive with a given (functional) upper bound provided the necessary weighted
isoperimetric inequalities implied by Stokes are satisfied. We apply this to
prove a comparison predicted by Gromov between the cofilling function and the
filling area.Comment: The new features of the main result are its sharpness and the fact
that the manifold is not assumed have bounded geometry, nor even to be
complete. This paper corresponds to a part of a talk given in January 2004 in
Haifa, at a workshop in memory of Robert Brooks. The other part, which is the
"translation" in the framework of geometric group theory, will soon be
deposited on arxi
