Periodic manifolds with spectral gaps |
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Authors: | Olaf Post |
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Institution: | Institut für Reine und Angewandte Mathematik, Rheinisch-Westfälische Technische, Hochschule Aachen, Templergraben 55, 52062 Aachen, Germany |
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Abstract: | We investigate spectral properties of the Laplace operator on a class of non-compact Riemannian manifolds. For a given number N we construct periodic manifolds such that the essential spectrum of the corresponding Laplacian has at least N open gaps. We use two different methods. First, we construct a periodic manifold starting from an infinite number of copies of a compact manifold, connected by small cylinders. In the second construction we begin with a periodic manifold which will be conformally deformed. In both constructions, a decoupling of the different period cells is responsible for the gaps. |
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Keywords: | Laplacian on a Riemannian manifold Spectral gaps Periodic manifolds Operation of a discrete group on a manifold |
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