Related papers: Limits of limit sets II: Geometrically Infinite Gr…

There are sequences of directions such that, given any compact set K in R^n, the sequence of iterated Steiner symmetrals of K in these directions converges to a ball. However examples show that Steiner symmetrization along a sequence of…

We establish vanishing results for limits of characters in various discrete groups, most notably irreducible lattices in higher rank semisimple Lie groups. As an application, we show that any sequence of finite-dimensional representations…

Given a metric (graph) bundle $X$ over $B$ where all the fibres are strongly relatively hyperbolic and nonelementary we show that, under certain conditions, $X$ is strongly hyperbolic relative to a collection of maximal cone-subbundles of…

In this article, we prove a version of Martin and Skora's conjecture that convergence groups on the $2$-sphere are covered by Kleinian groups. Given a relatively hyperbolic group pair $(G,\mathcal{P})$ with planar boundary and no Sierpinski…

This is an expository paper. We prove the Cannon-Thurston property for bounded geometry surface groups with or without punctures. We prove three theorems, due to Cannon-Thurston, Minsky and Bowditch. The proofs are culled out of earlier…

We characterize the rigidity of Carnot groups in the class of $C^2$ contact maps in terms of complex characteristics. Furthermore, we obtain a Liouville type theorem for Carnot groups which states that 1-quasiconformal maps form finite…

We show that the topology of uniform convergence on bounded sets is compatible with the group law of the automorphism group of a large class of spaces that are endowed with both a uniform structure and a bornology, thus yielding numerous…

In this paper, we prove a limit set intersection theorem in relatively hyperbolic groups. Our approach is based on a study of dynamical quasiconvexity of relatively quasiconvex subgroups. Using dynamical quasiconvexity, many well-known…

We continue here the investigation of the relationship between the intersection of a pair of subgroups of a Kleinian group, and in particular the limit set of that intersection, and the intersection of the limit sets of the subgroups. Of…

We describe isotropic orbits for the restricted action of a subgroup of a Lie group acting on a symplectic manifold by Hamiltonian symplectomorphisms and admitting an Ad*-equivariant moment map. We obtain examples of Lagrangian orbits of…

Let $G$ be a real reductive Lie group, $L$ a compact subgroup, and $\pi$ an irreducible admissible representation of $G$. In this article we prove a necessary and sufficient condition for the finiteness of the multiplicities of $L$-types…

We show that up to commensurability there are only finitely many cocompact arithmetic Kleinian groups generated by rotations. This implies, in particular, that there exist only finitely many conjugacy classes of cocompact two generated…

The Burton--Keane theorem for the almost-sure uniqueness of infinite clusters is a landmark of stochastic geometry. Let $\mu$ be a translation-invariant probability measure with the finite-energy property on the edge-set of a…

We demonstrate the convergence of the characteristic polynomial of several random matrix ensembles to a limiting universal function, at the microscopic scale. The random matrix ensembles we treat are classical compact groups and the…

We correct an error in the paper [BLO3], and take the opportunity to examine in more detail the derived functors of inverse limits over orbit categories of (infinite) locally finite groups. The main results show how to reduce this in many…

In this paper, we introduce cosine Thurston maps. In particular, we construct postsingularly finite topological cosine maps and focus on such maps with strictly preperiodic critical points. We use the techniques of Hubbard, Schleicher, and…

Consider a general circle packing $\mathcal{P}$ in the complex plane $\mathbb{C}$ invariant under a Kleinian group $\Gamma$. When $\Gamma$ is convex-cocompact or its critical exponent is greater than 1, we obtain an effective…

I study Gromov-Hausdorff limits of complex curves endowed with singular flat metrics of constant diameter. I formulate a criterion that the limit is collapsed in terms of a certain piecewise affine weight function on the dual intersection…

In the setting of CAT(k) spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky-Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric…

In \cite{Elek} we proved that the limit of a weakly convergent sequence of finite graphs can be viewed as a graphing or a continuous field of infinite graphs. Thus one can associate a type $II_1$-von Neumann algebra to such graph sequences.…