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A natural Finsler-Laplace operator

Barthelmé, Thomas

In: Israel Journal of Mathematics, 2013, vol. 196, no. 1, p. 375-412

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    Titel
    • A natural Finsler-Laplace operator
    Autor
    • Barthelmé, Thomas. Institut de Mathématiques, Université de Neuchâtel, Rue Emile-Argand 11, 2000, Neuchâtel, Switzerland
    Dokumententyp
    • Postprint
    Sprache
    • Englisch
    Veröffentlicht in
    • Israel Journal of Mathematics, 2013, vol. 196, no. 1, p. 375-412. Springer US; http://www.springer-ny.com
    Andere elektronische Ausgabe
    Klassifikation
    • Mathematik
    OAI-PMH-ID
    • oai:doc.rero.ch:311502
    Summary
    We give a new definition of a Laplace operator for Finsler metric as an average with regard to an angle measure of the second directional derivatives. This definition uses a dynamical approach due to Foulon that does not require the use of connections or local coordinates. We give explicit representations and computations of spectral data for this operator in the case of Katok-Ziller metrics on the sphere and the torus