Metric limits of manifolds with positive scalar curvature
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
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| _version_ | 1866915023285125120 |
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| author | Lee, Man-Chun Topping, Peter M. |
| author_facet | Lee, Man-Chun Topping, Peter M. |
| contents | We show that any Riemannian metric conformal to the round metric on $S^n$, for $n\geq 4$, arises as a limit of a sequence of Riemannian metrics of positive scalar curvature on $S^n$ in the sense of uniform convergence of Riemannian distance. In particular, non-negativity of scalar curvature is not preserved under such limits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_01223 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Metric limits of manifolds with positive scalar curvature Lee, Man-Chun Topping, Peter M. Differential Geometry Metric Geometry 53C21 We show that any Riemannian metric conformal to the round metric on $S^n$, for $n\geq 4$, arises as a limit of a sequence of Riemannian metrics of positive scalar curvature on $S^n$ in the sense of uniform convergence of Riemannian distance. In particular, non-negativity of scalar curvature is not preserved under such limits. |
| title | Metric limits of manifolds with positive scalar curvature |
| topic | Differential Geometry Metric Geometry 53C21 |
| url | https://arxiv.org/abs/2203.01223 |