On the interplay between inverse scattering for asymptotically hyperbolic manifolds and the Calderón problem for the Conformal Laplacian
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909977239617536 |
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| author | Muñoz-Thon, Sebastián |
| author_facet | Muñoz-Thon, Sebastián |
| contents | In this short note, we use the relation obtained by Guillarmou--Guillopé and Chang--González between the generalized eigenvalue problem for asymptotically hyperbolic (AH) manifolds and the Conformal Laplacian, to obtain a new inverse scattering result: on an AH manifold of dimension $n+1$ with constant scalar curvature $-n(n+1)$, we show that the scattering matrix at energy $\frac{n+1}{2}$ determines the jet of the metric on the boundary, up to a diffeomorphism and conformal factor. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_16646 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the interplay between inverse scattering for asymptotically hyperbolic manifolds and the Calderón problem for the Conformal Laplacian Muñoz-Thon, Sebastián Analysis of PDEs Differential Geometry Spectral Theory 35R30, 58J50, 35P25 In this short note, we use the relation obtained by Guillarmou--Guillopé and Chang--González between the generalized eigenvalue problem for asymptotically hyperbolic (AH) manifolds and the Conformal Laplacian, to obtain a new inverse scattering result: on an AH manifold of dimension $n+1$ with constant scalar curvature $-n(n+1)$, we show that the scattering matrix at energy $\frac{n+1}{2}$ determines the jet of the metric on the boundary, up to a diffeomorphism and conformal factor. |
| title | On the interplay between inverse scattering for asymptotically hyperbolic manifolds and the Calderón problem for the Conformal Laplacian |
| topic | Analysis of PDEs Differential Geometry Spectral Theory 35R30, 58J50, 35P25 |
| url | https://arxiv.org/abs/2507.16646 |