SCATTERING RIGIDITY FOR ANALYTIC METRICS

The paper proves that for real-analytic compact manifolds with analytic strictly convex boundary, no conjugate points, and hyperbolic trapped set, equality of the scattering data under a fixed boundary identification yields a boundary-fixing analytic isometry; notably, travel time is not required (Theorem 2 and the surrounding discussion emphasize this point) . The model’s solution is logically sound but proceeds via an extra step: it first recovers the travel time using the exactness identity S*α∂ − α∂ = dτ and the fact that τ vanishes on the glancing set—facts consistent with the paper’s setup, where τg is defined, analytic off Γg−, and equals 0 on ∂+SM ∪ ∂0SM , and where Sg is defined as the boundary scattering map . The final step then invokes the same scattering rigidity theorem. Hence both reach the same conclusion, but the paper’s proof is different and does not use the reduction to lens data.