We define the p-dimensional
collar Colp(M,g) of a compact torsion-free Riemannian manifold (M,g) to be the
greatest lower bound of the masses of all the p-dimensional currents which represent
non-trivial integral homology classes. When the cohomology ring of M satisfies a
certain non-degeneracy condition there is an inequality giving a lower bound on the
volume of (M,g) in terms of certain p-dimensional collars of (M,g). This is a
version of the stable isosystolic inequality using currents rather than singular
homology.
In addition to deriving this version of the stable isosystolic inequality, we show for
one class of manifolds that it is a sharp inequality.
