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The spectrum of the Laplacian on forms over flat manifolds

  • Nelia CharalambousEmail author
  • Zhiqin Lu
Article
  • 6 Downloads

Abstract

In this article we prove that the spectrum of the Laplacian on k-forms over a non compact flat manifold is always a connected closed interval of the non negative real line. The proof is based on a detailed decomposition of the structure of flat manifolds.

Keywords

Essential spectrum Hodge Laplacian Flat manifolds 

Mathematics Subject Classification

Primary 58J50 Secondary 53C35 

Notes

Acknowledgements

The authors would like to thank V. Kapovich and R. Mazzeo for their feedback and useful discussions regarding the structure of flat manifolds. They are also grateful to J. Lott for helping them work out Example 2.4.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of CyprusNicosiaCyprus
  2. 2.Department of MathematicsUniversity of CaliforniaIrvineUSA

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