Absence of principal eigenvalues for higher rank locally symmetric spaces
Weich, Tobias
Wolf, Lasse Lennart
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.
2022
info:eu-repo/semantics/preprint
doc-type:preprint
text
http://purl.org/coar/resource_type/c_816b
https://ris.uni-paderborn.de/record/31189
Weich T, Wolf LL. Absence of principal eigenvalues for higher rank locally symmetric spaces. <i>arXiv:220503167</i>. Published online 2022.
eng
info:eu-repo/semantics/altIdentifier/arxiv/2205.03167
info:eu-repo/semantics/closedAccess