7 citations · 14 across the 10 of their papers we have counts for
16 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…
Convex cocompact groups with three-dimensional limit sets
Sami Douba, Gye-Seon Lee, Ludovic Marquis +1
We provide a general construction of convex cocompact hyperbolic reflection groups with three-dimensional limit sets. More precisely, our construction takes as input an arbitrary s…
Zariski-Closures of Linear Reflection Groups
Jacques Audibert, Sami Douba, Gye-Seon Lee +1
We give necessary and sufficient conditions for a linear reflection group in the sense of Vinberg to be Zariski-dense in the ambient projective general linear group. As an applicat…
Convex cocompact groups in real hyperbolic spaces with limit set a Pontryagin sphere
Sami Douba, Gye-Seon Lee, Ludovic Marquis +1
We exhibit two examples of convex cocompact subgroups of the isometry groups of real hyperbolic spaces with limit set a Pontryagin sphere: one generated by reflections of $\ma…
Discrete Coxeter groups
Gye-Seon Lee, Ludovic Marquis
Coxeter groups are a special class of groups generated by involutions. They play important roles in the various areas of mathematics. This survey particularly focuses on how one us…
Deformation spaces of Coxeter truncation polytopes
Suhyoung Choi, Gye-Seon Lee, Ludovic Marquis
A convex polytope in the real projective space with reflections in the facets of is a Coxeter polytope if the reflections generate a subgroup of the group of projective…
Convex cocompactness for Coxeter groups
Jeffrey Danciger, François Guéritaud, Fanny Kassel +2
We investigate representations of Coxeter groups into as geometric reflection groups which are convex cocompact in the projective space $\mathbb{P}(\mat…
A small closed convex projective 4-manifold via Dehn filling
Gye-Seon Lee, Ludovic Marquis, Stefano Riolo
In order to obtain a closed orientable convex projective four-manifold with small positive Euler characteristic, we build an explicit example of convex projective Dehn filling of a…
Anti-de Sitter strictly GHC-regular groups which are not lattices
Gye-Seon Lee, Ludovic Marquis
For , we exhibit examples of strictly GHC-regular groups which are not quasi-isometric to the hyperbolic space , nor to any symm…
Surface groups of diffeomorphisms of the interval
Ludovic Marquis, Juan Souto
We prove that the group of diffeomorphisms of the interval contains surface groups whose action on has no global fix point, is topologically transitive, and such th…
Convex projective generalized Dehn filling
Suhyoung Choi, Gye-Seon Lee, Ludovic Marquis
For , we exhibit the first examples of complete finite volume hyperbolic -manifolds with cusps such that infinitely many -orbifolds obtained from b…
Properly convex bending of hyperbolic manifolds
Samuel A. Ballas, Ludovic Marquis
In this paper we show that bending a finite volume hyperbolic -manifold along a totally geodesic hypersurface results in a properly convex projective structure on wi…
Deformations of convex real projective manifolds and orbifolds
Suhyoung Choi, Gye-Seon Lee, Ludovic Marquis
In this survey, we study representations of finitely generated groups into Lie groups, focusing on the deformation spaces of convex real projective structures on closed manifolds a…
Entropy rigidity of Hilbert and Riemannian metrics
Thomas Barthelmé, Ludovic Marquis, Andrew Zimmer
In this paper we provide two new characterizations of real hyperbolic -space using the Poincaré exponent of a discrete group and the volume growth entropy. The first characteriz…
Coxeter group in Hilbert geometry
Ludovic Marquis
A theorem of Tits - Vinberg allows to build an action of a Coxeter group on a properly convex open set of the real projective space, thanks to the data of a polytope an…
Around groups in Hilbert Geometry
Ludovic Marquis
This is survey about action of group on Hilbert geometry. It will be a chapter of the "Handbook of Hilbert geometry" edited by G. Besson, M. Troyanov and A. Papadopoulos.