6 citations · 17 across the 10 of their papers we have counts for
11 papers
On 4-dimensional convex projective domains invariant by a lattice of
Ludovic Marquis, Pierre-Louis Blayac
This paper is a sequel to the erratum by the authors to a paper by Crampon and Marquis (see arXiv:1202.5442). The main result of the Erratum was relating several notions of geometr…
Hitchin grafting representations I: Geometry
Pierre-Louis Blayac, Ursula Hamenstädt, Théo Marty
We give a geometric interpretation of Fock--Goncharov positivity and show that bending deformations of Fuchsian representations stabilize a uniform Finsler quasi-convex disk in the…
Hitchin grafting representations II: Dynamics
Pierre-Louis Blayac, Ursula Hamenstädt, Théo Marty +1
The Hitchin component of the character variety of representations of a surface group into for some can be equipped with a pressure…
Counting, mixing and equidistribution for GPS systems with applications to relatively Anosov groups
Pierre-Louis Blayac, Richard Canary, Feng Zhu +1
We establish counting, mixing and equidistribution results for finite BMS measures on flow spaces associated to geometrically finite convergence group actions. We show that, in par…
Patterson-Sullivan theory for coarse cocycles
Pierre-Louis Blayac, Richard Canary, Feng Zhu +1
In this paper we develop a theory of Patterson--Sullivan measures associated to coarse cocycles of convergence groups. This framework includes Patterson-Sullivan measures associate…
Divisible convex sets with properly embedded cones
Pierre-Louis Blayac, Gabriele Viaggi
In this article we construct many examples of properly convex irreducible domains divided by Zariski dense relatively hyperbolic groups in every dimension at least 3. This answers…
The boundary of rank-one divisible convex sets
Pierre-Louis Blayac
We prove that for any non-symmetric irreducible divisible convex set, the proximal limit set is the full projective boundary.
Patterson--Sullivan densities in convex projective geometry
Pierre-Louis Blayac
For any rank-one convex projective manifold with a compact convex core, we prove that there exists a unique probability measure of maximal entropy on the set of unit tangent vector…
Ergodicity and equidistribution in Hilbert geometry
Pierre-Louis Blayac, Feng Zhu
We show that dynamical and counting results characteristic of negatively-curved Riemannian geometry, or more generally CAT() or rank-one CAT() spaces, also hold for rank-one…
Topological mixing of the geodesic flow on convex projective manifolds
Pierre-Louis Blayac
We introduce a natural subset of the unit tangent bundle of a convex projective manifold, the biproximal unit tangent bundle; it is closed and invariant under the geodesic flow, an…
Finitude géométrique en géométrie de Hilbert + an erratum/addendum
Pierre-Louis Blayac, Mickaël Crampon, Ludovic Marquis
The paper is divided in 2 parts. The first part is the original paper of the second and third authors arXiv:1202.5442v2. The second part is an erratum/addendum written in english a…