On the essential spectrum of differential operators over geometrically finite orbifolds

TL;DR

This paper investigates the essential spectrum of elliptic differential operators on geometrically finite orbifolds, providing insights into their spectral properties in a geometric setting.

Contribution

It characterizes the essential spectrum of first-order and Laplace-type operators on Riemannian orbifolds with geometric finiteness, extending spectral theory to orbifold contexts.

Findings

Determined the essential spectrum for a class of elliptic operators on orbifolds.

Extended spectral analysis techniques to geometrically finite orbifolds.

Provided foundational results for spectral geometry on orbifolds.

Abstract

We discuss the essential spectrum of essentially self-adjoint elliptic differential operators of first order and of Laplace type operators on Riemannian vector bundles over geometrically finite orbifolds.