A natural Finsler--Laplace operator

Details A natural Finsler--Laplace operator A natural Finsler--Laplace operator

2011-04-21

arxiv.org/abs/1104.4326v2

Mathematics

Differential Geometry

25 pages, v2: minor modifications, changed the introduction

Scientific paper

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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