Boundary determination and local rigidity of analytic metrics in the Lorentzian scattering rigidity problem
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912065835237376 |
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| author | Stefanov, Plamen |
| author_facet | Stefanov, Plamen |
| contents | We study the scattering rigidity problem in Lorentzian geometry: recovery of a Lorentzian metric from the scattering relation known on a lateral timelike boundary. We show that one can recover the jet of the metric up to a gauge transformation near a lightlike strictly convex point. Assuming that the metric is real analytic, we show that one can recover the metric up to a gauge transformation as well near such a point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15541 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundary determination and local rigidity of analytic metrics in the Lorentzian scattering rigidity problem Stefanov, Plamen Differential Geometry Analysis of PDEs 35R30, 53C24, 53B30 We study the scattering rigidity problem in Lorentzian geometry: recovery of a Lorentzian metric from the scattering relation known on a lateral timelike boundary. We show that one can recover the jet of the metric up to a gauge transformation near a lightlike strictly convex point. Assuming that the metric is real analytic, we show that one can recover the metric up to a gauge transformation as well near such a point. |
| title | Boundary determination and local rigidity of analytic metrics in the Lorentzian scattering rigidity problem |
| topic | Differential Geometry Analysis of PDEs 35R30, 53C24, 53B30 |
| url | https://arxiv.org/abs/2404.15541 |