Large group actions on manifolds.
Cross ratios, surface groups, and diffeomorphisms of the circle
This article relates representations of surface groups to cross ratios. We first identify a connected component of the space of representations into PSL(,ℝ) – known as the -– to a subset of the set of cross ratios on the boundary at infinity of the group. Similarly, we study some representations into associated to cross ratios and exhibit a “character variety” of these representations. We show that this character variety contains all-Hitchin components as well as the set of negatively curved metrics...
Une relation entre diamètre extrinsèque, intégrale de la courbe de Gauss et inradius pour les hypersurfaces localement convexes d'un espace euclidien.
Problème de Minkowski et surfaces à courbure constante dans les variétés hyperboliques
Cross ratios, Anosov representations and the energy functional on Teichmüller space
We study two classes of linear representations of a surface group: Hitchin and maximal symplectic representations. We relate them to cross ratios and thus deduce that they are which means that their translation lengths are roughly controlled by the translations lengths on the Cayley graph. As a consequence, we show that the mapping class group acts properly on the space of representations and that the energy functional associated to such a representation is proper. This implies the existence of...
Sur les espaces homogènes modèles de variétés compactes
Sur les variétés compactes asymptotiquement hamroniques.
Sur les difféomorphismes d'Anosov affines à feuilletages stable et instable différentiables.
Flots d'Anosov à distributions de Liapounov différentiables. I
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