{"type":"preprint","citation":{"mla":"Delarue, Benjamin, et al. “Spectra of Lorentzian Quasi-Fuchsian Manifolds.” <i>ArXiv:2504.21762</i>, 2025.","bibtex":"@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} }","ieee":"B. Delarue, C. Guillarmou, and D. Monclair, “Spectra of Lorentzian quasi-Fuchsian manifolds,” <i>arXiv:2504.21762</i>. 2025.","chicago":"Delarue, Benjamin, Colin Guillarmou, and Daniel Monclair. “Spectra of Lorentzian Quasi-Fuchsian Manifolds.” <i>ArXiv:2504.21762</i>, 2025.","apa":"Delarue, B., Guillarmou, C., &#38; Monclair, D. (2025). Spectra of Lorentzian quasi-Fuchsian manifolds. In <i>arXiv:2504.21762</i>.","short":"B. Delarue, C. Guillarmou, D. Monclair, ArXiv:2504.21762 (2025).","ama":"Delarue B, Guillarmou C, Monclair D. Spectra of Lorentzian quasi-Fuchsian manifolds. <i>arXiv:250421762</i>. Published online 2025."},"publication":"arXiv:2504.21762","date_updated":"2025-05-12T08:18:06Z","_id":"59860","title":"Spectra of Lorentzian quasi-Fuchsian manifolds","language":[{"iso":"eng"}],"author":[{"full_name":"Delarue, Benjamin","last_name":"Delarue","id":"70575","first_name":"Benjamin"},{"first_name":"Colin","full_name":"Guillarmou, Colin","last_name":"Guillarmou"},{"last_name":"Monclair","full_name":"Monclair, Daniel","first_name":"Daniel"}],"user_id":"70575","year":"2025","date_created":"2025-05-12T08:17:23Z","status":"public","abstract":[{"text":"A three-dimensional quasi-Fuchsian Lorentzian manifold $M$ is a globally\r\nhyperbolic spacetime diffeomorphic to $\\Sigma\\times (-1,1)$ for a closed\r\norientable surface $\\Sigma$ of genus $\\geq 2$. It is the quotient\r\n$M=\\Gamma\\backslash \\Omega_\\Gamma$ of an open set $\\Omega_\\Gamma\\subset {\\rm\r\nAdS}_3$ by a discrete group $\\Gamma$ of isometries of ${\\rm AdS}_3$ which is a\r\nparticular example of an Anosov representation of $\\pi_1(\\Sigma)$. We first\r\nshow that the spacelike geodesic flow of $M$ is Axiom A, has a discrete Ruelle\r\nresonance spectrum with associated (co-)resonant states, and that the\r\nPoincar\\'e series for $\\Gamma$ extend meromorphically to $\\mathbb{C}$. This is\r\nthen used to prove that there is a natural notion of resolvent of the\r\npseudo-Riemannian Laplacian $\\Box$ of $M$, which is meromorphic on $\\mathbb{C}$\r\nwith poles of finite rank, defining a notion of quantum resonances and quantum\r\nresonant states related to the Ruelle resonances and (co-)resonant states by a\r\nquantum-classical correspondence. This initiates the spectral study of convex\r\nco-compact pseudo-Riemannian locally symmetric spaces.","lang":"eng"}],"external_id":{"arxiv":["2504.21762"]}}