{"citation":{"chicago":"Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues for Higher Rank Locally Symmetric  Spaces.” <i>Communications in Mathematical Physics</i> 403 (2023). <a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>.","bibtex":"@article{Weich_Wolf_2023, title={Absence of principal eigenvalues for higher rank locally symmetric  spaces}, volume={403}, DOI={<a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>}, journal={Communications in Mathematical Physics}, author={Weich, Tobias and Wolf, Lasse Lennart}, year={2023} }","ama":"Weich T, Wolf LL. Absence of principal eigenvalues for higher rank locally symmetric  spaces. <i>Communications in Mathematical Physics</i>. 2023;403. doi:<a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>","short":"T. Weich, L.L. Wolf, Communications in Mathematical Physics 403 (2023).","apa":"Weich, T., &#38; Wolf, L. L. (2023). Absence of principal eigenvalues for higher rank locally symmetric  spaces. <i>Communications in Mathematical Physics</i>, <i>403</i>. <a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>","ieee":"T. Weich and L. L. Wolf, “Absence of principal eigenvalues for higher rank locally symmetric  spaces,” <i>Communications in Mathematical Physics</i>, vol. 403, 2023, doi: <a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>.","mla":"Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues for Higher Rank Locally Symmetric  Spaces.” <i>Communications in Mathematical Physics</i>, vol. 403, 2023, doi:<a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>."},"user_id":"49178","department":[{"_id":"10"},{"_id":"548"},{"_id":"623"}],"abstract":[{"lang":"eng","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."}],"doi":"https://doi.org/10.1007/s00220-023-04819-1","volume":403,"language":[{"iso":"eng"}],"publication_identifier":{"unknown":["1275-1295"]},"_id":"31189","intvolume":"       403","year":"2023","date_updated":"2024-02-06T20:52:40Z","author":[{"first_name":"Tobias","orcid":"0000-0002-9648-6919","id":"49178","full_name":"Weich, Tobias","last_name":"Weich"},{"last_name":"Wolf","full_name":"Wolf, Lasse Lennart","id":"45027","first_name":"Lasse Lennart"}],"status":"public","publication":"Communications in Mathematical Physics","date_created":"2022-05-11T10:38:11Z","title":"Absence of principal eigenvalues for higher rank locally symmetric  spaces","external_id":{"arxiv":["2205.03167"]},"type":"journal_article"}