The spectrum of the Laplacian on forms over flat manifolds

The spectrum of the Laplacian on forms over flat manifolds

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.

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Veröffentlicht in:Mathematische Zeitschrift 2020-10, Vol.296 (1-2), p.1-12
Hauptverfasser: Charalambous, Nelia, Lu, Zhiqin
Format: Artikel
Sprache:eng
Schlagworte:
Manifolds
Mathematics
Mathematics and Statistics
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Zusammenfassung: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.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-019-02407-5