$L^p$-Spectral theory of locally symmetric spaces with $Q$-rank one

TL;DR

This paper investigates the $L^p$-spectral properties of the Laplace-Beltrami operator on specific locally symmetric spaces with finite volume and rank one cusps, extending results to more general manifolds with similar cusp structures.

Contribution

It provides new insights into the $L^p$-spectral theory for locally symmetric spaces of rank one and generalizes these results to manifolds with rank one cusps.

Findings

Characterization of the $L^p$-spectrum for these spaces

Extension of spectral results to manifolds with rank one cusps

Identification of spectral properties related to the geometry of the space

Abstract

We study the $L^p$-spectrum of the Laplace-Beltrami operator on certain complete locally symmetric spaces $M=\Gamma\backslash X$ with finite volume and arithmetic fundamental group $\Gamma$ whose universal covering $X$ is a symmetric space of non-compact type. We also show, how the obtained results for locally symmetric spaces can be generalized to manifolds with cusps of rank one.