3 citations · 8 across the 9 of their papers we have counts for
12 papers
Critical exponents of normal subgroups in higher rank
Olivier Glorieux, Samuel Tapie
We study the critical exponents of discrete subgroups of a higher rank semi-simple real linear Lie group . Let us fix a Cartan subspace of the L…
Random triangles on flat tori
Olivier Glorieux, Andrew Yarmola
Inspired by classical puzzles in geometry that ask about probabilities of geometric phenomena, we give an explicit formula for the probability that a random triangle on a flat toru…
The Dirichlet random walk
Adrien Boulanger, Olivier Glorieux
In this article we define and study a stochastic process on Galoisian covers of compact manifolds. The successive positions of the process are defined recursively by picking a poin…
The embedding of the space of negatively curved surfaces in geodesic currents
Olivier Glorieux
We prove by an algebraic method that the embedding of the Teichmuller space in the space of geodesic currents is totally linearly independent. We prove a similar result for all neg…
Hausdorff dimension of limit sets for projective Anosov representations
Olivier Glorieux, Daniel Monclair, Nicolas Tholozan
We study the relation between critical exponents and Hausdorff dimensions of limit sets for projective Anosov representations. We prove that the Hausdorff dimension of the symmetri…
Topological mixing of the Weyl chamber flow
Nguyen-Thi Dang, Olivier Glorieux
In this paper, we study topological properties of the right action by translation of the Weyl Chamber flow on the space of Weyl chambers. We obtain a necessary and sufficient condi…
Regularity of limit sets of AdS quasi-Fuchsian groups
Olivier Glorieux, Daniel Monclair
Limit sets of -quasi-Fuchsian groups of are always Lipschitz submanifolds. The aim of this article is to show that they are never ,…
Critical exponent for geodesic currents
Olivier Glorieux
For any geodesic current we associated a quasi-metric space. For a subclass of geodesic currents, called filling, it defines a metric and we study the critical exponent associated…
Convergence of quasi-Fuchsian groups using critical exponent
Olivier Glorieux
We prove that a sequence of quasi-Fuchsian representations for which the critical exponent converges to the topological dimension of the boundary of the group (larger than 2), conv…
Critical exponent and Hausdorff dimension in pseudo-Riemannian hyperbolic geometry
Olivier Glorieux, Daniel Monclair
The aim of this article is to understand the geometry of limit sets in pseudo-Riemannian hyperbolic geometry. We focus on a class of subgroups of introduced by…
Entropy of embedded surfaces in quasi-fuchsian manifolds
Olivier Glorieux
We compare critical exponent for quasi-Fuchsian groups acting on the hyperbolic 3-space, , and on invariant disks embedded in . We give a rigidity theor…
Counting closed geodesics in globally hyperbolic maximal compact AdS 3-manifolds
Olivier Glorieux
We propose a definition for the length of closed geodesics in a globally hyperbolic maximal compact (GHMC) Anti-De Sitter manifold. We then prove that the number of closed geodesic…