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Partial Differential Equations and Spectral Theory pp 251–260Cite as

Birkhäuser

Periodic Manifolds, Spectral Gaps, and Eigenvalues in Gaps

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 126))

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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Author information

Authors and Affiliations

  1. Rheinisch-Westfälische Technische Hochschule Aachen, Institut für Reine und Angewandte Mathematik, Templergraben 55, Aachen, 52062, Germany

    Olaf Post

Authors
  1. Olaf Post
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, TU Clausthal, Erzstr. 1, Clausthal-Zellerfeld, 38678, Germany

    Michael Demuth

  2. Institut für Mathematik, Universität Potsdam, Am Neuen Palais 10, Potsdam, 14469, Germany

    Bert-Wolfgang Schulze

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© 2001 Springer Basel AG

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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

  • eBook Packages: Springer Book Archive

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