Simplicial volume and 0-strata of separating filtrations

We use Papasoglu’s method of area-minimizing separating sets to give an alternative proof, and explicit constants, for the following theorem of Guth and Braun–Sauer: If [Formula: see text] is a closed, oriented, connected [Formula: see text]-dimensional manifold, with a Riemannian metric such that every ball of radius [Formula: see text] in the universal cover of [Formula: see text] has volume at most [Formula: see text], then the simplicial volume of [Formula: see text] is at most the volume of [Formula: see text] times a constant depending on [Formula: see text] and [Formula: see text].