A splitting theorem for 3-manifold with nonnegative scalar curvature and mean-convex boundary
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909465036455936 |
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| author | Hong, Han Wang, Gaoming |
| author_facet | Hong, Han Wang, Gaoming |
| contents | We show that a Riemannian 3-manifold with nonnegative scalar curvature and mean-convex boundary is flat if it contains an absolutely area-minimizing (in the free boundary sense) half-cylinder or strip. Analogous results also hold for a $θ$-energy-minimizing half-cylinder, or, under certain topological assumptions, a $θ$-energy-minimizing strip for $θ\in (0,π)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08677 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A splitting theorem for 3-manifold with nonnegative scalar curvature and mean-convex boundary Hong, Han Wang, Gaoming Differential Geometry We show that a Riemannian 3-manifold with nonnegative scalar curvature and mean-convex boundary is flat if it contains an absolutely area-minimizing (in the free boundary sense) half-cylinder or strip. Analogous results also hold for a $θ$-energy-minimizing half-cylinder, or, under certain topological assumptions, a $θ$-energy-minimizing strip for $θ\in (0,π)$. |
| title | A splitting theorem for 3-manifold with nonnegative scalar curvature and mean-convex boundary |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2501.08677 |