The space of rough Riemannian metrics
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908448920174592 |
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| author | Bandara, Lashi Hassan, Anisa |
| author_facet | Bandara, Lashi Hassan, Anisa |
| contents | On a smooth connected manifold, we consider all possible locally elliptic and locally bounded measurable coefficient Riemannian metrics called rough Riemannian metrics. We equip this set with an extended metric which is connected if and only if the manifold is compact. We prove that this is a complete length extended metric space and the components on which the distance is finite are path-connected. Moreover, we identify the closure of smooth metrics in this space to be continuous metrics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10274 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The space of rough Riemannian metrics Bandara, Lashi Hassan, Anisa Differential Geometry Functional Analysis Metric Geometry 53C23, 58A05, 58D17 On a smooth connected manifold, we consider all possible locally elliptic and locally bounded measurable coefficient Riemannian metrics called rough Riemannian metrics. We equip this set with an extended metric which is connected if and only if the manifold is compact. We prove that this is a complete length extended metric space and the components on which the distance is finite are path-connected. Moreover, we identify the closure of smooth metrics in this space to be continuous metrics. |
| title | The space of rough Riemannian metrics |
| topic | Differential Geometry Functional Analysis Metric Geometry 53C23, 58A05, 58D17 |
| url | https://arxiv.org/abs/2507.10274 |