On the Spectrum of Certain Hadamard Manifolds

TL;DR

This paper investigates the spectral properties of certain Hadamard manifolds, establishing the absolute continuity of their spectra and explicitly characterizing the spectrum for specific classes and quotients.

Contribution

It provides new results on the spectrum's structure and continuity for particular Hadamard manifolds and their quotients, expanding understanding in geometric spectral theory.

Findings

Proved the absolute continuity of the spectrum for two classes of Hadamard manifolds.

Determined the spectrum as a set for these classes and specific domains.

Analyzed spectral properties of quotients of Hadamard manifolds.

Abstract

We show the absolute continuity of the spectrum and determine the spectrum as a set for two classes of Hadamard manifolds and for specific domains and quotients of one of the classes.