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| We study an inverse scattering problem on asymptotically hyperbolic Liouville surfaces and prove uniqueness of such surfaces (up to isometries consistent with the Liouville structure) from the knowledge of the scattering matrix at a fixed energy associated with scalar waves. The main ingredients to prove this result are the separability of the wave equation into a system of ODEs, the Complex Angular Momentum method and a reinterpretation of the partial scattering coefficients as generalized Weyl-Titchmarsh functions for a certain Sturm-Liouville equation having the complex angular momentum as spectral parameter. |
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