Absence of principal eigenvalues for higher rank locally symmetric spaces
T. Weich, L.L. Wolf, ArXiv:2205.03167 (2022).
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Abstract
Given a geometrically finite hyperbolic surface of infinite volume it is a
classical result of Patterson that the positive Laplace-Beltrami operator has
no $L^2$-eigenvalues $\geq 1/4$. In this article we prove a generalization of
this result for the joint $L^2$-eigenvalues of the algebra of commuting
differential operators on Riemannian locally symmetric spaces $\Gamma\backslash
G/K$ of higher rank. We derive dynamical assumptions on the $\Gamma$-action on
the geodesic and the Satake compactifications which imply the absence of the
corresponding principal eigenvalues. A large class of examples fulfilling these
assumptions are the non-compact quotients by Anosov subgroups.
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arXiv:2205.03167
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Weich T, Wolf LL. Absence of principal eigenvalues for higher rank locally symmetric spaces. arXiv:220503167. Published online 2022.
Weich, T., & Wolf, L. L. (2022). Absence of principal eigenvalues for higher rank locally symmetric spaces. In arXiv:2205.03167.
@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} }
Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues for Higher Rank Locally Symmetric Spaces.” ArXiv:2205.03167, 2022.
T. Weich and L. L. Wolf, “Absence of principal eigenvalues for higher rank locally symmetric spaces,” arXiv:2205.03167. 2022.
Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues for Higher Rank Locally Symmetric Spaces.” ArXiv:2205.03167, 2022.