{"author":[{"id":"49178","full_name":"Weich, Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","first_name":"Tobias"},{"first_name":"Lasse Lennart","full_name":"Wolf, Lasse Lennart","id":"45027","last_name":"Wolf"}],"_id":"31189","date_created":"2022-05-11T10:38:11Z","status":"public","language":[{"iso":"eng"}],"type":"preprint","external_id":{"arxiv":["2205.03167"]},"year":"2022","abstract":[{"text":"Given a geometrically finite hyperbolic surface of infinite volume it is a\r\nclassical result of Patterson that the positive Laplace-Beltrami operator has\r\nno $L^2$-eigenvalues $\\geq 1/4$. In this article we prove a generalization of\r\nthis result for the joint $L^2$-eigenvalues of the algebra of commuting\r\ndifferential operators on Riemannian locally symmetric spaces $\\Gamma\\backslash\r\nG/K$ of higher rank. We derive dynamical assumptions on the $\\Gamma$-action on\r\nthe geodesic and the Satake compactifications which imply the absence of the\r\ncorresponding principal eigenvalues. A large class of examples fulfilling these\r\nassumptions are the non-compact quotients by Anosov subgroups.","lang":"eng"}],"publication":"arXiv:2205.03167","department":[{"_id":"10"},{"_id":"548"}],"user_id":"45027","citation":{"ieee":"T. Weich and L. L. Wolf, “Absence of principal eigenvalues for higher rank locally symmetric  spaces,” <i>arXiv:2205.03167</i>. 2022.","mla":"Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues for Higher Rank Locally Symmetric  Spaces.” <i>ArXiv:2205.03167</i>, 2022.","ama":"Weich T, Wolf LL. Absence of principal eigenvalues for higher rank locally symmetric  spaces. <i>arXiv:220503167</i>. Published online 2022.","short":"T. Weich, L.L. Wolf, ArXiv:2205.03167 (2022).","bibtex":"@article{Weich_Wolf_2022, title={Absence of principal eigenvalues for higher rank locally symmetric  spaces}, journal={arXiv:2205.03167}, author={Weich, Tobias and Wolf, Lasse Lennart}, year={2022} }","apa":"Weich, T., &#38; Wolf, L. L. (2022). Absence of principal eigenvalues for higher rank locally symmetric  spaces. In <i>arXiv:2205.03167</i>.","chicago":"Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues for Higher Rank Locally Symmetric  Spaces.” <i>ArXiv:2205.03167</i>, 2022."},"title":"Absence of principal eigenvalues for higher rank locally symmetric  spaces","date_updated":"2022-05-24T12:25:29Z"}