02-309 Olaf Post

Eigenvalues in Spectral Gaps of a Perturbed Periodic Manifold (172K, LaTeX2e with 3 PS-Figures (30 pages)) Jul 14, 02

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Abstract. 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.

Files: 02-309.src( 02-309.keywords , eigenvalues.tex , figure-1.eps , figure-2.eps , figure-3.eps )