Abstract
We investigate spectral properties of the Laplace operator on a class of non-compact Riemannian manifolds. We prove that for a given number N we can construct a periodic manifold such that the essential spectrum of the corresponding Laplacian has at least N open gaps. Furthermore, by perturbing the periodic metric of the manifold locally we can prove the existence of eigenvalues in a gap of the essential spectrum.
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Post, O. (2001). Periodic Manifolds, Spectral Gaps, and Eigenvalues in Gaps. In: Demuth, M., Schulze, BW. (eds) Partial Differential Equations and Spectral Theory. Operator Theory: Advances and Applications, vol 126. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8231-6_29
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DOI: https://doi.org/10.1007/978-3-0348-8231-6_29
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9483-8
Online ISBN: 978-3-0348-8231-6
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