Invertibility of local geodesic transverse and mixed ray transforms I: basic cases
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910299650523136 |
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| author | Uhlmann, Gunther Zhai, Jian |
| author_facet | Uhlmann, Gunther Zhai, Jian |
| contents | Consider a compact Riemannian manifold in dimension $n\geq 3$ with strictly convex boundary. We show that the transverse ray transform of $1$ tensors and the mixed ray transform of $1+1$ tensors are invertible, up to natural obstructions, near a boundary point. When the manifold admits a strictly convex function, this local invertibility result leads to a global result by a layer stripping argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09017 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Invertibility of local geodesic transverse and mixed ray transforms I: basic cases Uhlmann, Gunther Zhai, Jian Differential Geometry 53C22, 53C65 Consider a compact Riemannian manifold in dimension $n\geq 3$ with strictly convex boundary. We show that the transverse ray transform of $1$ tensors and the mixed ray transform of $1+1$ tensors are invertible, up to natural obstructions, near a boundary point. When the manifold admits a strictly convex function, this local invertibility result leads to a global result by a layer stripping argument. |
| title | Invertibility of local geodesic transverse and mixed ray transforms I: basic cases |
| topic | Differential Geometry 53C22, 53C65 |
| url | https://arxiv.org/abs/2401.09017 |