Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only! Grab it Explore a mathematical lecture examining the stability of spectra under coverings, focusing on Riemannian manifolds and eigenfunction analysis. Delve into whether eigenfunctions on manifold M with eigenvalues in (0,Λ) exist independently of pull-backs from manifold N when considering a Riemannian covering p:M→N of closed Riemannian manifolds. Learn from Werner Ballmann's collaborative research with Sugata Mondal as they present various approaches and solutions to this fundamental question in spectral geometry.