Rigidity in fixed angle inverse scattering for Riemannian metrics
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908398138687488 |
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| author | Oksanen, Lauri Rakesh Salo, Mikko |
| author_facet | Oksanen, Lauri Rakesh Salo, Mikko |
| contents | The fixed angle inverse scattering problem for a velocity consists in determining a sound speed, or a Riemannian metric up to diffeomorphism, from measurements obtained by probing the medium with a single plane wave. This is a formally determined inverse problem that is open in general. In this article we consider the rigidity question of distinguishing a sound speed or a Riemannian metric from the Euclidean metric. We prove that a general smooth metric that is Euclidean outside a ball can be distinguished from the Euclidean metric. The methods involve distorted plane waves and a combination of geometric, topological and unique continuation arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06864 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rigidity in fixed angle inverse scattering for Riemannian metrics Oksanen, Lauri Rakesh Salo, Mikko Analysis of PDEs 35R30 The fixed angle inverse scattering problem for a velocity consists in determining a sound speed, or a Riemannian metric up to diffeomorphism, from measurements obtained by probing the medium with a single plane wave. This is a formally determined inverse problem that is open in general. In this article we consider the rigidity question of distinguishing a sound speed or a Riemannian metric from the Euclidean metric. We prove that a general smooth metric that is Euclidean outside a ball can be distinguished from the Euclidean metric. The methods involve distorted plane waves and a combination of geometric, topological and unique continuation arguments. |
| title | Rigidity in fixed angle inverse scattering for Riemannian metrics |
| topic | Analysis of PDEs 35R30 |
| url | https://arxiv.org/abs/2410.06864 |