2025/04/09 by Sardà, Teo Gil Moreno de Mora
#Differential Geometry (math.DG) #FOS: Mathematics #Primary 53C23 #Secondary 53C21
paper · doi:10.48550/arxiv.2504.06737
We prove that if a complete Riemannian n-manifold with non-trivial codimension 1 homology with ℤ2-coefficients or ℤ-coefficients has positive macroscopic scalar curvature large enough, then it contains a non-nullhomologous hypersurface of small Urysohn (n-2)-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.