Urysohn width of Hypersurfaces and Positive Macroscopic Scalar Curvature

We prove that if a complete Riemannian [Formula: see text]-manifold with non-trivial codimension 1 homology with [Formula: see text]-coefficients or [Formula: see text]-coefficients has positive macroscopic scalar curvature large enough, then it contains a non-nullhomologous hypersurface of small Urysohn [Formula: see text]-width. This constitutes a macroscopic analogue of a theorem by Bray–Brendle–Neves on the area of non-contractible 2-spheres in a closed Riemannian 3-manifold with positive scalar curvature. Our proof is based on an adaptation of Guth’s macroscopic version of the Schoen–Yau descent argument.