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On the multiplicy of the eigenvalues of the Laplacian

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Geometry and Analysis on Manifolds

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1339))

Abstract

The recent progress in the study of multiplicities of the eigenvalues of the Laplacian has brought through new ideas, in particular the link between the operator theory on graphs and operator theory on manifolds. This has lead to a complete solution of the original problem in dimension greater than 2. The case of Dimension 2 is still open, but the conjecture mentioned above is an aim to reach.

Many other problems are left in connection to what has been presented here. Let us briefly describe some of them.

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Authors
  1. Gérard Besson
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Toshikazu Sunada

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© 1988 Springer-Verlag

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Besson, G. (1988). On the multiplicy of the eigenvalues of the Laplacian. In: Sunada, T. (eds) Geometry and Analysis on Manifolds. Lecture Notes in Mathematics, vol 1339. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083045

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  • DOI: https://doi.org/10.1007/BFb0083045

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50113-8

  • Online ISBN: 978-3-540-45930-9

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