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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2504.06737 |
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| _version_ | 1866912318162468864 |
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| author | Sardà, Teo Gil Moreno de Mora |
| author_facet | Sardà, Teo Gil Moreno de Mora |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06737 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Urysohn width of hypersurfaces and positive macroscopic scalar curvature Sardà, Teo Gil Moreno de Mora Differential Geometry Primary 53C23, Secondary 53C21 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. |
| title | Urysohn width of hypersurfaces and positive macroscopic scalar curvature |
| topic | Differential Geometry Primary 53C23, Secondary 53C21 |
| url | https://arxiv.org/abs/2504.06737 |