@article{31189,
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.}},
author = {{Weich, Tobias and Wolf, Lasse Lennart}},
journal = {{Communications in Mathematical Physics}},
title = {{{Absence of principal eigenvalues for higher rank locally symmetric spaces}}},
doi = {{https://doi.org/10.1007/s00220-023-04819-1}},
volume = {{403}},
year = {{2023}},
}