Level sets of harmonic functions on three-dimensional manifolds with nonnegative scalar curvature
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908527510945792 |
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| author | Sun, Yukai |
| author_facet | Sun, Yukai |
| contents | We investigate the level sets of harmonic functions on $(\mathbb{R}^{3}\setminus \{0\},g)$. Drawing inspiration from Miao, we adopt the method developed by Munteanu-Wang to derive a monotonic quantity associated with the level sets of harmonic functions on $(\mathbb{R}^{3}\setminus \{0\},g)$ with nonnegative scalar curvature, under certain conditions. Furthermore, we establish a rigidity result for this quantity. Additionally, we find an extra scalar-flat metric on $\mathbb{R}^{3}\setminus \{0\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07608 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Level sets of harmonic functions on three-dimensional manifolds with nonnegative scalar curvature Sun, Yukai Differential Geometry We investigate the level sets of harmonic functions on $(\mathbb{R}^{3}\setminus \{0\},g)$. Drawing inspiration from Miao, we adopt the method developed by Munteanu-Wang to derive a monotonic quantity associated with the level sets of harmonic functions on $(\mathbb{R}^{3}\setminus \{0\},g)$ with nonnegative scalar curvature, under certain conditions. Furthermore, we establish a rigidity result for this quantity. Additionally, we find an extra scalar-flat metric on $\mathbb{R}^{3}\setminus \{0\}$. |
| title | Level sets of harmonic functions on three-dimensional manifolds with nonnegative scalar curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2509.07608 |