Preprints and Recent Publications

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On integral geometry in projective Finsler spaces
by Rolf Schneider

This paper extends the Crofton formulas of Alvarez and Fernandes for smooth projective Finsler spaces to rectifiable Borel subsets in these spaces.

Electronic version.


Comportements asymptotiques et rigidités en géométries de Hilbert
by Edith Socié-Méthou

This paper contains a detailed study of the Hilbert geometries. These geometries are natural generalizations of real hyperbolic space and as such play an important role in Finsler and metric geometry. Among Socié-Méthou's results we find that two Hilbert geometries contain a pair of isometric open sets if and only if they are globally isometric and that the set of isometries of a Hilbert geometry with suitably smooth and convex boundary is noncompact if and only if this boundary is an ellipsoid.

Comportements asymptotiques et rigidités en géométries de Hilbert is available electronically as a gzipped ps file.

Entropies et métriques de Finsler
by Patrick Vérovic

This paper studies the topological and volume entropy of Finsler metrics with special emphasis on symmetric Finsler spaces of noncompact type and rank greater than one. In this case, Vérovic finds a very simple formula for the volume entropy and shows that the Riemannian symmetric metric does not minimize the normalized volume entropy among all invariant Finsler metrics.

In the last chapter, Vérovic turns to the study of the topological entropy of Finsler metrics on symmetric spaces of rank one. In this case he proves that hyperbolic metrics are critical points for the topological entropy if it is normalized with the Hausdorff measure (or Busemann volume). This result also holds if the dimension of the manifold is two and the entropy is normalized with the Holmes-Thompson volume, which is called the Liouville volume in this work.

Entropies et métriques de Finsler is available electronically as a gzipped ps file.