Complete stable minimal hypersurfaces in positively curved 4-manifolds
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913197958627328 |
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| author | Chodosh, Otis Li, Chao Stryker, Douglas |
| author_facet | Chodosh, Otis Li, Chao Stryker, Douglas |
| contents | We show that the combination of non-negative sectional curvature (or $2$-intermediate Ricci curvature) and strict positivity of scalar curvature forces rigidity of complete (non-compact) two-sided stable minimal hypersurfaces in a $4$-manifold with bounded curvature. In particular, this implies the nonexistence of complete two-sided stable minimal hypersurface in a closed $4$-manifold with positive sectional curvature.
Our work leads to new comparison results. We also construct various examples showing rigidity of stable minimal hypersurfaces can fail under other curvature conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_07708 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Complete stable minimal hypersurfaces in positively curved 4-manifolds Chodosh, Otis Li, Chao Stryker, Douglas Differential Geometry We show that the combination of non-negative sectional curvature (or $2$-intermediate Ricci curvature) and strict positivity of scalar curvature forces rigidity of complete (non-compact) two-sided stable minimal hypersurfaces in a $4$-manifold with bounded curvature. In particular, this implies the nonexistence of complete two-sided stable minimal hypersurface in a closed $4$-manifold with positive sectional curvature. Our work leads to new comparison results. We also construct various examples showing rigidity of stable minimal hypersurfaces can fail under other curvature conditions. |
| title | Complete stable minimal hypersurfaces in positively curved 4-manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2202.07708 |