Topology of 3-manifolds with nonnegative scalar curvature and positive harmonic functions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866908949538668544 |
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| author | Yan, Zetian Zhu, Xingyu |
| author_facet | Yan, Zetian Zhu, Xingyu |
| contents | We study complete $3$-manifolds with nonnegative scalar curvature under additional regularity assumptions. We prove that a contractible such manifold is diffeomorphic to $\mathbb{R}^3$, and that an open handlebody admitting such a metric must have genus at most $1$. The proof uses exhaustions by level sets of harmonic functions and refined average gradient estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08285 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topology of 3-manifolds with nonnegative scalar curvature and positive harmonic functions Yan, Zetian Zhu, Xingyu Differential Geometry 53C21, 53C24, 57K10 We study complete $3$-manifolds with nonnegative scalar curvature under additional regularity assumptions. We prove that a contractible such manifold is diffeomorphic to $\mathbb{R}^3$, and that an open handlebody admitting such a metric must have genus at most $1$. The proof uses exhaustions by level sets of harmonic functions and refined average gradient estimates. |
| title | Topology of 3-manifolds with nonnegative scalar curvature and positive harmonic functions |
| topic | Differential Geometry 53C21, 53C24, 57K10 |
| url | https://arxiv.org/abs/2604.08285 |