Daniel Monclair
A three-dimensional quasi-Fuchsian Lorentzian manifold $M$ is a globally hyperbolic spacetime diffeomorphic to $\Sigma\times (-1,1)$ for a closed orientable surface $\Sigma$ of genus $\geq 2$. It is the quotient $M=\Gamma\backslash…
Given a non-compact semisimple real Lie group $G$ and an Anosov subgroup $\Gamma$, we utilize the correspondence between $\mathbb R$-valued additive characters on Levi subgroups $L$ of $G$ and $\mathbb R$-affine homogeneous line bundles…
By constructing a non-empty domain of discontinuity in a suitable homogeneous space, we prove that every torsion-free projective Anosov subgroup is the monodromy group of a locally homogeneous contact Axiom A dynamical system with a unique…
Limit sets of $\mathrm{AdS}$-quasi-Fuchsian groups of $\mathrm{PO}(n,2)$ are always Lipschitz submanifolds. The aim of this article is to show that they are never $\mathcal{C}^1$, except for the case of Fuchsian groups. As a byproduct we…
We consider hyperbolic and anti-de Sitter (AdS) structures on $M\times (0,1)$, where $M$ is a $d$-dimensional Gromov-Thurston manifold. If $M$ has cone angles greater than $2\pi$, we show that there exists a "quasifuchsian" (globally…
We study the geometry of a weak Riemannian metric on the infinite dimensional manifold of compact spacelike Cauchy hypersurfaces in a globally hyperbolic spacetime. We show that the geodesic distance (i.e. the infimum of lengths of paths…
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 symmetric limit set in $\mathbf{P}(\mathbb{R}^{n}) \times…
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 $\mathrm{PO}(p,q+1)$ introduced by Danciger, Gu\'eritaud and Kassel, called…
We develop a new approach to the existence of time functions on Lorentzian manifolds, based on Conley's work regarding Lyapunov functions for dynamical systems. We recover Hawking's result that a stably causal admits a time function through…
We study groups of circle diffeomorphisms whose action on the cylinder $\mathcal C=\mathbb S^1\times \mathbb S^1\setminus \Delta$ preserves a volume form. We first show that such a group is topologically conjugate to a subgroup of…
We study a simple problem that arises from the study of Lorentz surfaces and Anosov flows. For a non decreasing map of degree one $h:\mathbb{S}^1\to \mathbb{S}^1$, we are interested in groups of circle diffeomorphisms that act on the…
We study the isometry group of a globally hyperbolic spatially compact Lorentz surface. Such a group acts on the circle, and we show that when the isometry group acts non properly, the subgroups of $\mathrm{Diff}(\mathbb{S}^1)$ obtained are…