Bounds on primitives of differential forms and cofilling inequalities
Abstract
Description
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.
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 arxiv
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 arxiv