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A natural Finsler--Laplace operator

By Thomas Barthelmé

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.Comment: 25 pages, v2: minor modifications, changed the introductio

Topics: Mathematics - Differential Geometry, 58J60, 53C60
Year: 2012
DOI identifier: 10.1007/s11856-012-0168-z
OAI identifier: oai:arXiv.org:1104.4326
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