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Eigenvalue control for a Finsler-Laplace operator

Barthelmé, Thomas ; Colbois, Bruno

In: Annals of Global Analysis and Geometry, 2013, vol. 44, no. 1, p. 43-72

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    Titel
    • Eigenvalue control for a Finsler-Laplace operator
    Autor
    • Barthelmé, Thomas. Institut de Mathématiques, Université de Neuchâtel, Neuchâtel, Switzerland
    • Colbois, Bruno. Institut de Mathématiques, Université de Neuchâtel, Neuchâtel, Switzerland
    Dokumententyp
    • Postprint
    Sprache
    • Englisch
    Veröffentlicht in
    • Annals of Global Analysis and Geometry, 2013, vol. 44, no. 1, p. 43-72. Springer Netherlands
    Andere elektronische Ausgabe
    OAI-PMH-ID
    • oai:doc.rero.ch:309631
    Summary
    Using the definition of a Finsler-Laplacian given by the first author, we show that two bi-Lipschitz Finsler metrics have a controlled spectrum. We deduce from that several generalizations of Riemannian results. In particular, we show that the spectrum on Finsler surfaces is controlled above by a constant depending on the topology of the surface and on the quasireversibility constant of the metric. In contrast to Riemannian geometry, we then give examples of highly non-reversible metrics on surfaces with arbitrarily large first eigenvalue