 02309 Olaf Post
 Eigenvalues in Spectral Gaps of a Perturbed Periodic Manifold
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Jul 14, 02

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Abstract. We consider a noncompact 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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