A splitting theorem for manifolds with spectral nonnegative Ricci curvature and mean-convex boundary
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866908808721203200 |
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| author | Hong, Han Wang, Gaoming |
| author_facet | Hong, Han Wang, Gaoming |
| contents | We prove a splitting theorem for a smooth noncompact manifold with (possibly noncompact) boundary. We show that if a noncompact manifold of dimension $n\geq 2$ has $λ_1(-αΔ+\operatorname{Ric})\geq 0$ for some $α<\frac{4}{n-1}$ and mean-convex boundary, then it is either isometric to $Σ\times \mathbb{R}_{\geq 0}$ for a closed manifold $Σ$ with nonnegative Ricci curvature or it has no interior ends. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07009 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A splitting theorem for manifolds with spectral nonnegative Ricci curvature and mean-convex boundary Hong, Han Wang, Gaoming Differential Geometry We prove a splitting theorem for a smooth noncompact manifold with (possibly noncompact) boundary. We show that if a noncompact manifold of dimension $n\geq 2$ has $λ_1(-αΔ+\operatorname{Ric})\geq 0$ for some $α<\frac{4}{n-1}$ and mean-convex boundary, then it is either isometric to $Σ\times \mathbb{R}_{\geq 0}$ for a closed manifold $Σ$ with nonnegative Ricci curvature or it has no interior ends. |
| title | A splitting theorem for manifolds with spectral nonnegative Ricci curvature and mean-convex boundary |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2503.07009 |