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

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 $4{\lambda }_1>h^2$, where ${\lambda }_1$ is the bottom of the $L^2$-spectrum and $h$ the topological entropy of the flow.

Comments welcome. v2: Remove an unnecessary hypothesis in Theorem 1, added Proposition 19, minor changes in the text

References in corpus (1)

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