The spectrum of the Laplacian on forms over flat manifolds
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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.
KeywordsEssential spectrum Hodge Laplacian Flat manifolds
Mathematics Subject ClassificationPrimary 58J50 Secondary 53C35
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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