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arXiv · 1104.4326

A natural Finsler--Laplace operator

Thomas Barthelmé
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Abstract

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 nor local coordinates. We show using 1-parameter families of Katok--Ziller metrics that this Finsler--Laplace operator admits explicit representations and computations of spectral data.

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Thomas Barthelmé. 2012-02-20. A natural Finsler--Laplace operator. https://doi.org/10.1007/s11856-012-0168-z

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