Related papers: Kleinian groups which are almost fuchsian

We compare two families of left-invariant metrics on a surface group $\Gamma=\pi_1(\Sigma)$ in the context of course-geometry. One family comes from Riemannian metrics of negative curvature on the the surface $\Sigma$, and another from…

We study unions of fundamental domains of a Fuchsian group, especially those with hyperbolic plane metric realizing the metric of the corresponding hyperbolic surface. We call these unions the \textit{geodesic covers} of the Fuchsian group…

We consider 3-dimensional hyperbolic cone-manifolds, singular along infinite lines, which are ``convex co-compact'' in a natural sense. We prove an infinitesimal rigidity statement when the angle around the singular lines is less than…

In this paper, we study the topology of the boundaries of quasi-Fuchsian spaces. We first show for a given convergent sequence of quasi-Fuchsian groups, how we can know the end invariant of the limit group from the information on the…

Quasifuchsian hyperbolic manifolds, or more generally convex co-compact hyperbolic manifolds, have infinite volume, but they have a well-defined ``renormalized'' volume. We outline some relations between this renormalized volume and the…

We examine the dependence of the deformation obtained by bending quasi-Fuchsian structures on the bending lamination. We show that when we consider bending quasi-Fuchsian structures on a closed surface, the conditions obtained by Epstein…

We study the fuzzy spaces (as special examples of noncommutative manifolds) with their quasicoherent states in order to find their pertinent metrics. We show that they are naturally endowed with two natural "quantum metrics" which are…

We establish a uniformization result for metric surfaces - metric spaces that are topological surfaces with locally finite Hausdorff 2-measure. Using the geometric definition of quasiconformality, we show that a metric surface that can be…

We study the geometry of nonrelatively hyperbolic groups. Generalizing a result of Schwartz, any quasi-isometric image of a non-relatively hyperbolic space in a relatively hyperbolic space is contained in a bounded neighborhood of a single…

We show that on every manifold, every conformal class of semi-Riemannian metrics contains a metric $g$ such that each $k$-th-order covariant derivative of the Riemann tensor of $g$ has bounded absolute value $a_k$. This result is new also…

We prove that a Kleinian surface groups is determined, up to conjugacy in the isometry group of $\mathbb H^3$, by its simple marked length spectrum. As a first application, we show that a discrete faithful representation of the fundamental…

This article was born as a generalisation of the analysis made by Series, where she made the first attempt to plot a deformation space of Kleinian group of more than 1 complex dimension. We use the Top Terms' Relationship proved by the…

A Kleinian group $\Gamma < \mathrm{Isom}(\mathbb H^3)$ is called convex cocompact if any orbit of $\Gamma$ in $\mathbb H^3$ is quasiconvex or, equivalently, $\Gamma$ acts cocompactly on the convex hull of its limit set in $\partial \mathbb…

An association scheme is called quasi-thin if the valency of each its basic relation is one or two. A quasi-thin scheme is Kleinian if the thin residue of it forms a Klein group with respect to the relation product. It is proved that any…

Let S be a compact surface of genus >1, and g be a metric on S of constant curvature K\in\{-1,0,1\} with conical singularities of negative singular curvature. When K=1 we add the condition that the lengths of the contractible geodesics are…

We compare critical exponent for quasi-Fuchsian groups acting on the hyperbolic 3-space, $\mathbb{H}^3$, and on invariant disks embedded in $\mathbb{H}^3$. We give a rigidity theorem for all embedded surfaces when the action is Fuchsian and…

For a space $X$, let $(CL(X), \tau_V)$, $(CL(X), \tau_{locfin})$ and $(CL(X), \tau_F)$ be the set $CL(X)$ of all nonempty closed subsets of $X$ which are endowed with Vietoris topology, locally finite topology and Fell topology…

We define a pseudometric on the set of all unbounded subsets of a metric space. The Kolmogorov quotient of this pseudometric space is a complete metric space. The definition of the pseudometric is guided by the principle that two unbounded…

We study the medial axis of a set $K$ in Euclidean space (the set of points in space with more than one closest point in $K$) from a "coarse" and "quantitative" perspective. We show that on "most" balls $B(x,r)$ in the complement of $K$,…

We develop a new orbit equivalence framework for holomorphically mating the dynamics of complex polynomials with that of Kleinian surface groups. We show that the only torsion-free Fuchsian groups that can be thus mated are punctured sphere…