That is, systolic invariants or products of systolic invariants do not in general provide universal (i.e. curvature-free) lower bounds for the total volume of a closed Riemannian manifold.
preprint in 1992 (which eventually appeared as Gromov 1996), and was further developed by Mikhail Katz, Michael Freedman and others.
Croke & Katz (2003) survey the main results on systolic freedom.
The complex projective plane admits Riemannian metrics of arbitrarily small volume, such that every essential surface is of area at least 1.
Here a surface is called "essential" if it cannot be contracted to a point in the ambient 4-manifold.