5 citations · 16 across the 10 of their papers we have counts for
15 papers
Properness of the bending map
Cyril Lecuire
The bending map of a hyperbolic 3-manifold with boundary maps a geometrically hyperbolic metric to its bending measured geodesic lamination. We show that the bending map is proper.…
Homoclinic leaves, Hausdorff limits and homeomorphisms
Ian Biringer, Cyril Lecuire
We show that except for one exceptional case, a lamination on the boundary of a 3-dimensional handlebody H is a Hausdorff limit of meridians if and only if it is commensurable to a…
Thurston's Bounded image theorem
Cyril Lecuire, Ken'ichi Ohshika
Thurston's bounded image theorem is one of the key steps in his proof of the uniformisation theorem for Haken manifolds. Thurston never published its proof, and no proof has been k…
The Double Limit Theorem and its Legacy
Cyril Lecuire
This chapter surveys recent and less recent results on convergence of Kleinian representations, following Thurston's Double Limit and "AH(acylindrical) is compact" Theorems.
Quasi-isometric rigidity of three manifold groups
Peter Haïssinsky, Cyril Lecuire
We provide a proof that the classes of finitely generated Kleinian groups and of three-manifold groups are quasi-isometrically rigid.
An extension of the Masur domain
Cyril Lecuire
The Masur domain is a subset of the space of projective measured geodesic laminations on the boundary of a 3-manifold M. This domain plays an important role in the study of the hyp…
Horospheres in degenerate 3-manifolds
Cyril Lecuire, Mahan Mj
We study horospheres in hyperbolic 3-manifolds all whose ends are degenerate. Towards this, we study which almost minimizing geodesics in go through arbitrarily thin parts.
Convergence and divergence of Kleinian surface groups
Jeffrey Brock, Kenneth Bromberg, Richard Canary +1
We characterize sequences of Kleinian surface groups with convergent subsequences in terms of the asymptotic behavior of the ending invariants of the associated hyperbolic 3-manifo…
Primitive stable closed hyperbolic 3-manifolds
Inkang Kim, Cyril Lecuire, Ken'ichi Ohshika
We show that closed 3-manifolds with high Heegaard distance and bounded subsurface Heegaard distance are primitive stable when they are regarded as representations from the free gr…
Convexity of strata in diagonal pants graphs of surfaces
Javier Aramayona, Cyril Lecuire, Hugo Parlier +1
We prove a number of convexity results for strata of the diagonal pants graph of a surface, in analogy with the extrinsic geometric properties of strata in the Weil-Petersson compl…
Primitive stable representations of free Kleinian groups
W. Jeon, I. Kim, K. Ohshika with C. Lecuire
In this paper, we give a complete criterion for a discrete faithful representation $ρ:F_n \ra \pslc$ to be primitive stable. This will answer Minsky's conjectures about geometric c…
Strong convergence of Kleinian groups: the cracked eggshell
James W. Anderson, Cyril Lecuire
In this paper we give a complete description of the set of discrete faithful representations SH(M) uniformizing a compact, orientable, hyperbolizable 3-manifold M with incompressib…
The convex core of quasifuchsian manifolds with particles
Cyril Lecuire, Jean-Marc Schlenker
We consider quasifuchsian manifolds with "particles", i.e., cone singularities of fixed angle less than going from one connected component of the boundary at infinity to the ot…
Convergence of freely decomposable Kleinian groups
Inkang Kim, Cyril Lecuire, Ken'ichi Ohshika
We consider a compact orientable hyperbolic 3-manifold with a compressible boundary. Suppose that we are given a sequence of geometrically finite hyperbolic metrics whose conformal…
Continuity of the bending map
Cyril Lecuire
The bending map of a hyperbolic 3-manifold maps a convex cocompact hyperbolic metric on a hyperbolic 3-manifold with boundary to its bending measured geodesic lamination. In the pr…