On deformations of the spectrum of a Finsler--Laplacian that preserve the length spectrum

Thomas Barthelmé

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arXiv · 1410.1069

On deformations of the spectrum of a Finsler--Laplacian that preserve the length spectrum

Thomas Barthelmé

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Abstract

In this article, we show that a Finsler--Laplacian introduced previously can detect changes in the Finsler metric that the marked length spectrum cannot. We also construct examples of non-reversible Finsler metrics in negative curvature such that $4λ_1 > h^2$, where $λ_1$ is the bottom of the $L^2$-spectrum and $h$ the topological entropy of the flow.

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Thomas Barthelmé. 2015-06-22. On deformations of the spectrum of a Finsler--Laplacian that preserve the length spectrum. https://arxiv.org/abs/1410.1069

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