25 citations · 84 across the 23 of their papers we have counts for
6 papers · 1 filter
Entropy rigidity of Hilbert and Riemannian metrics
Thomas Barthelmé, Ludovic Marquis, Andrew Zimmer
In this paper we provide two new characterizations of real hyperbolic -space using the Poincaré exponent of a discrete group and the volume growth entropy. The first characteriz…
On deformations of the spectrum of a Finsler--Laplacian that preserve the length spectrum
Thomas Barthelmé
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…
Laplacian and spectral gap in regular Hilbert geometries
Thomas Barthelmé, Bruno Colbois, Mickaël Crampon +1
We study the spectrum of the Finsler--Laplace operator for regular Hilbert geometries, defined by convex sets with boundaries. We show that for an -dimensional geometry, t…
Eigenvalues control for a Finsler--Laplace operator
Thomas Barthelmé, Bruno Colbois
Using the definition of a Finsler--Laplacian given by the first author, we show that two bi-Lipschitz Finsler metrics have a controlled spectrum. We deduce from that several genera…
A new Laplace operator in Finsler geometry and periodic orbits of Anosov flows
Thomas Barthelmé
In the first part of this dissertation, 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…
A natural Finsler--Laplace operator
Thomas Barthelmé
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 dynami…