Bottom of spectra and coverings of orbifolds

TL;DR

This paper investigates how the lowest eigenvalue of scalar Schrödinger operators changes under Riemannian coverings of orbifolds, with applications to geometrically finite and conformally compact orbifolds.

Contribution

It provides new insights into the spectral behavior of Schrödinger operators on orbifolds under coverings, extending previous results to more general orbifold settings.

Findings

Characterization of the bottom of the spectrum under orbifold coverings

Application of results to geometrically finite orbifolds

Application of results to conformally compact orbifolds

Abstract

We discuss the behaviour of the bottom of the spectrum of scalar Schr\"odinger operators under Riemannian coverings of orbifolds. We apply our results to geometrically finite and to conformally compact orbifolds.