Related papers: The Bowditch boundary of $(G,\mathcal{H})$ when $G…

Suppose $G$ is a finitely generated group and $H$ is a subgroup of $G$. Let $\partial_{c}^{\mathcal{F}\mathcal{Q}}G$ denote the contracting boundary of $G$ with the topology of fellow travelling quasi-geodesics defined by Cashen-Mackay…

Let $G$ be a finitely presented group, and let $H$ be a subgroup of $G$. We prove that if $H$ is acylindrically hyperbolic and existentially closed in $G$, then $G$ is acylindrically hyperbolic. As a corollary, any finitely presented group…

Let $D=\{\rho < 0\}$ be a smooth relatively compact domain in an almost complex manifold $(M,J)$, where $\rho$ is a smooth defining function of $D$, strictly $J$-plurisubharmonic in a neighborhood of the closure $\overline{D}$ of $D$. We…

We prove a central limit theorem for the length of closed geodesics in any compact orientable hyperbolic surface. In the special case of a hyperbolic pair of pants, this settles a conjecture of Chas-Li-Maskit.

We prove some results concerning the boundary of a convex set in $\H^n$. This includes the convergence of curvature measures under Hausdorff convergence of the sets, the study of normal points, and, for convex surfaces, a generalized Gauss…

We prove a geometric criterion for the bounded multiplicity property of "small" infinite-dimensional representations of real reductive Lie groupsin both induction and restrictions. Applying the criterion to symmetric pairs, we give a full…

In this paper we give a complete description of the horofunction boundary of the infinite dimensional real hyperbolic space, and characterise its Busemann points.

Our first result gives a partial converse to a well-known theorem of A. Ancona for hyperbolic groups. We prove that a group $G$, equipped with a symmetric probability measure whose finite support generates $G$, is hyperbolic if it is…

Let (X_i,d_i), i=1,2, be proper geodesic hyperbolic metric spaces. We give a general construction for a ``hyperbolic product'' X_1{times}_h X_2 which is itself a proper geodesic hyperbolic metric space and examine its boundary at infinity.

Consider the following classes of pairs consisting of a group and a finite collection of subgroups: $\mathcal{C}= \left\{ (G,\mathcal H) \mid \text{$\mathcal{H}$ is hyperbolically embedded in $G$} \right\}$ and $ \mathcal{D}= \left\{…

Using a probabilistic argument we show that the second bounded cohomology of an acylindrically hyperbolic group $G$ (e.g., a non-elementary hyperbolic or relatively hyperbolic group, non-exceptional mapping class group, ${\rm Out}(F_n)$,…

We introduce the bounded packing property for a subgroup of a countable discrete group G. This property gives a finite upper bound on the number of left cosets of the subgroup that are pairwise close in G. We establish basic properties of…

This paper is devoted to confront two different approaches to the problem of dynam-ical perfect plasticity. Interpreting this model as a constrained boundary value Friedrichs' system enables one to derive admissible hyperbolic boundary…

The asymptotic bound for a length-based attack on the Conjugacy Search Problem in relatively hyperbolic groups is cubic for hyperbolic elements and a "small" polynomial for parabolic elements, depending on the Conjugacy Search Problem for…

In this paper, we study the Hausdorff dimension of the Floyd and Bowditch boundaries of a relatively hyperbolic group, and show that for the Floyd metric and shortcut metrics respectively, they are are both equal to a constant times the…

We look at tree amalgamations of locally finite quasi-transitive hyperbolic graphs and prove that the homeomorphism type of the hyperbolic boundary of such a tree amalgamation only depends on the homeomorphism types of the hyperbolic…

We consider the convergence of pointed multiply connected domains in the Caratheodory topology. Behaviour in the limit is largely determined by the properties of the simple closed hyperbolic geodesics which separate components of the…

We explain why it is necessary to use boundary conditions in the proof of supersymmetry of a supergravity action on a manifold with boundary. Working in both boundary (``downstairs'') and orbifold (``upstairs'') pictures, we present a…

Let $N$ be a geodesically convex subset in a convex co-compact hyperbolic manifold $M$ with incompressible boundary. We assume that each boundary component of $N$ is either a boundary component of $\partial_\infty M$, or a smooth, locally…

We will provide bounds on both the Betti numbers and the torsion part of the homology of hyperbolic orbifolds. These bounds are linear in the volume and are a direct consequence of an efficient simplicial model of the thick part, which we…