Stability for a class of three-tori with small negative scalar curvature
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929343196823552 |
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| author | Bryden, Edward Chen, Lizhi |
| author_facet | Bryden, Edward Chen, Lizhi |
| contents | We define a flexible class of Riemmanian metrics on the three-torus. Then, using Stern's inequality relating scalar curvature to harmonic one-forms, we show that any sequence of metrics in this family whose negative part of the scalar curvature tends to zero in $L^2$ norm has a subsequence which converges to some flat metric on the three-torus in the sense of Dong-Song. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12795 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability for a class of three-tori with small negative scalar curvature Bryden, Edward Chen, Lizhi Differential Geometry We define a flexible class of Riemmanian metrics on the three-torus. Then, using Stern's inequality relating scalar curvature to harmonic one-forms, we show that any sequence of metrics in this family whose negative part of the scalar curvature tends to zero in $L^2$ norm has a subsequence which converges to some flat metric on the three-torus in the sense of Dong-Song. |
| title | Stability for a class of three-tori with small negative scalar curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2404.12795 |