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arXiv · 2504.06737

Urysohn width of hypersurfaces and positive macroscopic scalar curvature

Teo Gil Moreno de Mora Sardà
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Abstract

We prove that if a complete Riemannian $n$-manifold with non-trivial codimension 1 homology with $\mathbb{Z}_2$-coefficients or $\mathbb{Z}$-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.

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Teo Gil Moreno de Mora Sardà. 2025-04-09. Urysohn width of hypersurfaces and positive macroscopic scalar curvature. https://arxiv.org/abs/2504.06737

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