2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57104We consider a non-compact Riemannian periodic manifold such that the corresponding Laplacian has a spectral gap. By continuously perturbing the periodic metric locally we can prove the existence of eigenvalues in a gap. A lower bound on the number of eigenvalue branches crossing a fixed level is established in terms of a discrete eigenvalue problem. Furthermore, we discuss examples of perturbations leading to infinitely many eigenvalue branches coming from above resp. finitely many branches coming from below.30 pages, 3 eps-figures, LaTeXMathematical PhysicsSpectral Theory35P20; 58J37text