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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.08189 |
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| _version_ | 1866912320661225472 |
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| author | Hsiao, Ming Lee, Man-Chun |
| author_facet | Hsiao, Ming Lee, Man-Chun |
| contents | In this work, we study a gap phenomenon in locally conformally flat Riemannian manifolds with non-negative Ricci curvature. We construct complete solutions to the Yamabe flow that exhibit instantaneous bounded curvature as they evolve. Using this, we demonstrate that if the curvature decays quickly enough in an integral sense, then the manifold must be flat. This partially generalizes the results of Chen-Zhu and Ma. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08189 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gap Theorem on locally conformally flat manifold Hsiao, Ming Lee, Man-Chun Differential Geometry In this work, we study a gap phenomenon in locally conformally flat Riemannian manifolds with non-negative Ricci curvature. We construct complete solutions to the Yamabe flow that exhibit instantaneous bounded curvature as they evolve. Using this, we demonstrate that if the curvature decays quickly enough in an integral sense, then the manifold must be flat. This partially generalizes the results of Chen-Zhu and Ma. |
| title | Gap Theorem on locally conformally flat manifold |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2504.08189 |