preprint Benjamin Delarue author 70575 Colin Guillarmou author Daniel Monclair author A three-dimensional quasi-Fuchsian Lorentzian manifold $M$ is a globally hyperbolic spacetime diffeomorphic to $\Sigma\times (-1,1)$ for a closed orientable surface $\Sigma$ of genus $\geq 2$. It is the quotient $M=\Gamma\backslash \Omega_\Gamma$ of an open set $\Omega_\Gamma\subset {\rm AdS}_3$ by a discrete group $\Gamma$ of isometries of ${\rm AdS}_3$ which is a particular example of an Anosov representation of $\pi_1(\Sigma)$. We first show that the spacelike geodesic flow of $M$ is Axiom A, has a discrete Ruelle resonance spectrum with associated (co-)resonant states, and that the Poincar\'e series for $\Gamma$ extend meromorphically to $\mathbb{C}$. This is then used to prove that there is a natural notion of resolvent of the pseudo-Riemannian Laplacian $\Box$ of $M$, which is meromorphic on $\mathbb{C}$ with poles of finite rank, defining a notion of quantum resonances and quantum resonant states related to the Ruelle resonances and (co-)resonant states by a quantum-classical correspondence. This initiates the spectral study of convex co-compact pseudo-Riemannian locally symmetric spaces. 2025 eng 2504.21762 Delarue B, Guillarmou C, Monclair D. Spectra of Lorentzian quasi-Fuchsian manifolds. <i>arXiv:250421762</i>. Published online 2025. @article{Delarue_Guillarmou_Monclair_2025, title={Spectra of Lorentzian quasi-Fuchsian manifolds}, journal={arXiv:2504.21762}, author={Delarue, Benjamin and Guillarmou, Colin and Monclair, Daniel}, year={2025} } Delarue, Benjamin, et al. “Spectra of Lorentzian Quasi-Fuchsian Manifolds.” <i>ArXiv:2504.21762</i>, 2025. B. Delarue, C. Guillarmou, D. Monclair, ArXiv:2504.21762 (2025). Delarue, Benjamin, Colin Guillarmou, and Daniel Monclair. “Spectra of Lorentzian Quasi-Fuchsian Manifolds.” <i>ArXiv:2504.21762</i>, 2025. Delarue, B., Guillarmou, C., &#38; Monclair, D. (2025). Spectra of Lorentzian quasi-Fuchsian manifolds. In <i>arXiv:2504.21762</i>. B. Delarue, C. Guillarmou, and D. Monclair, “Spectra of Lorentzian quasi-Fuchsian manifolds,” <i>arXiv:2504.21762</i>. 2025. 598602025-05-12T08:17:23Z2025-05-12T08:18:06Z