  We establish a min-max estimate on the volume width of a closed Riemannian
manifold with nonnegative Ricci curvature. More precisely, we show that every
closed Riemannian manifold with nonnegative Ricci curvature admits a PL Morse
function whose level set volume is bounded in terms of the volume of the
manifold. As a consequence of this sweep-out estimate, there exists an
embedded, closed (possibly singular) minimal hypersurface whose volume is
bounded in terms of the volume of the manifold.
