On the Spectral Theory and Dynamics of Asymptotically Hyperbolic Manifolds

The uploaded paper (Rowlett’s survey) states exactly the 0-trace wave trace formula on asymptotically hyperbolic manifolds with negative curvature and the Ehrenfest-time oscillatory bound as Theorem 5.1, with amplitude l(γ)/√|det(I−Pk_γ)| and a smooth remainder A(t), together with the long-time estimate |∫ A(t) cos(λt) ρ(t) dt| ≤ C for ρ supported in [t0, ε ln λ] and C depending only on t0 and ||ρ||∞ . It also recalls the Joshi–Sá Barreto construction of the wave group and the fact that the singular support of the 0-trace is contained in the length spectrum . The candidate solution reproduces the same statement and gives a plausible (but different) Egorov/Ehrenfest-time integration-by-parts argument. Minor caveat: the model’s sketch momentarily introduces derivative-dependence on ρ and then asserts it can be removed by smoothing/partitioning; the paper’s theorem claims dependence only on ||ρ||∞. Overall, the results match and the proofs differ in technique.