Invertibility of local geodesic transverse and mixed ray transforms II: higher order tensors
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916131906781184 |
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| author | Uhlmann, Gunther Zhai, Jian |
| author_facet | Uhlmann, Gunther Zhai, Jian |
| contents | Consider a compact Riemannian manifold in dimension $n$ with strictly convex boundary. We show the local invertibility near a boundary point of the transverse ray transform of $2$ tensors for $n\geq 3$ and the mixed ray transform of $2+2$ tensors for $n=3$. When the manifold admits a strictly convex function, this local invertibility result leads to global invertibility. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12640 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Invertibility of local geodesic transverse and mixed ray transforms II: higher order tensors Uhlmann, Gunther Zhai, Jian Differential Geometry Consider a compact Riemannian manifold in dimension $n$ with strictly convex boundary. We show the local invertibility near a boundary point of the transverse ray transform of $2$ tensors for $n\geq 3$ and the mixed ray transform of $2+2$ tensors for $n=3$. When the manifold admits a strictly convex function, this local invertibility result leads to global invertibility. |
| title | Invertibility of local geodesic transverse and mixed ray transforms II: higher order tensors |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2402.12640 |