The collars of a Riemannian manifold and stable isosystolic inequalities (Q1085460)

The author defines the p-dimensional collar of a compact torsion-free Riemannian manifold (M,g) to be the greatest lower bound of masses of all p-dimensional currents which represent nontrivial integral homology classes. Then he applies \textit{M. Gromov}'s isosystolic inequality [J. Differ. Geom. 18, 1-147 (1983; Zbl 0515.53037)] to obtain a lower bound on the volume of (M,g) in terms of certain p-dimensional collars of (M,g). For a spherical class of Riemannian manifolds, the author also shows that such lower bound on the volume of (M,g) is sharp.