A natural Finsler--Laplace operator

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.

25 pages, v2: minor modifications, changed the introduction

References in corpus (1)

• A new Laplace operator in Finsler geometry and periodic orbits of Anosov flows

Cited by in corpus (9)

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• Geodesic random walks, diffusion processes and Brownian motion on Finsler manifolds
• Eigenvalues control for a Finsler--Laplace operator
• Some fundamental problems in global Finsler geometry
• The maximum diam theorem on Finsler manifolds
• Semicontinuity of eigenvalues under intrinsic flat convergence
• Laplacian and spectral gap in regular Hilbert geometries
• On Lower Bounds of the First Eigenvalue of Finsler-Laplacian
• On deformations of the spectrum of a Finsler--Laplacian that preserve the length spectrum