Eigenvalues in Spectral Gaps of a Perturbed Periodic Manifold

Details Eigenvalues in Spectral Gaps of a Perturbed Periodic Manifold Eigenvalues in Spectral Gaps of a Perturbed Periodic Manifold

2002-07-14

arxiv.org/abs/math-ph/0207018v1

Physics

Mathematical Physics

30 pages, 3 eps-figures, LaTeX

Scientific paper

We 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.

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