The matrix weighted real-analytic double fibration transforms
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913170867617792 |
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| author | Chihara, Hiroyuki Jathar, Shubham R. Railo, Jesse |
| author_facet | Chihara, Hiroyuki Jathar, Shubham R. Railo, Jesse |
| contents | We show that the real-analytic matrix-weighted double fibration transform determines the analytic wavefront set of a vector-valued function. We apply this result to show that the matrix weighted ray transform is injective on a two-dimensional, non-trapping, real-analytic Riemannian manifold with strictly convex boundary. Additionally, we show that a real-analytic Higgs field can be uniquely determined from the nonabelian ray transform on real-analytic Riemannian manifolds of any dimension with a strictly convex boundary point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_24067 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The matrix weighted real-analytic double fibration transforms Chihara, Hiroyuki Jathar, Shubham R. Railo, Jesse Analysis of PDEs Differential Geometry Primary 44A12, Secondary 53C65, 58J40, 45Q05 We show that the real-analytic matrix-weighted double fibration transform determines the analytic wavefront set of a vector-valued function. We apply this result to show that the matrix weighted ray transform is injective on a two-dimensional, non-trapping, real-analytic Riemannian manifold with strictly convex boundary. Additionally, we show that a real-analytic Higgs field can be uniquely determined from the nonabelian ray transform on real-analytic Riemannian manifolds of any dimension with a strictly convex boundary point. |
| title | The matrix weighted real-analytic double fibration transforms |
| topic | Analysis of PDEs Differential Geometry Primary 44A12, Secondary 53C65, 58J40, 45Q05 |
| url | https://arxiv.org/abs/2506.24067 |