25 citations · 84 across the 23 of their papers we have counts for
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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…
Knot theory of R-covered Anosov flows: homotopy versus isotopy of closed orbits
Thomas Barthelmé, Sergio R. Fenley
In this article, we study the knots realized by periodic orbits of R-covered Anosov flows in compact 3-manifolds. We show that if two orbits are freely homotopic then in fact they…
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…