The Lorentzian Calderón problem on vector bundles
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914214739705856 |
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| author | Gomes, Sean Oksanen, Lauri |
| author_facet | Gomes, Sean Oksanen, Lauri |
| contents | In this paper we study a Lorentzian version of the Calderón problem, which is concerned with the determination of a connection and potential on a Hermitian vector bundle over a Lorentzian manifold from the Dirichlet-to-Neumann map of the associated connection wave operator. For a class of Lorentzian manifolds satisfying a curvature bound, including perturbations of Minkowski space over strictly convex domains, the connection and potential is shown to be uniquely determined up to the natural gauge transformations of the problem. The proof is based on ideas from the earlier works arXiv:2008.07508, arXiv:2112.01663 of the second author in the scalar setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19601 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Lorentzian Calderón problem on vector bundles Gomes, Sean Oksanen, Lauri Analysis of PDEs 35R30 In this paper we study a Lorentzian version of the Calderón problem, which is concerned with the determination of a connection and potential on a Hermitian vector bundle over a Lorentzian manifold from the Dirichlet-to-Neumann map of the associated connection wave operator. For a class of Lorentzian manifolds satisfying a curvature bound, including perturbations of Minkowski space over strictly convex domains, the connection and potential is shown to be uniquely determined up to the natural gauge transformations of the problem. The proof is based on ideas from the earlier works arXiv:2008.07508, arXiv:2112.01663 of the second author in the scalar setting. |
| title | The Lorentzian Calderón problem on vector bundles |
| topic | Analysis of PDEs 35R30 |
| url | https://arxiv.org/abs/2512.19601 |