We show that for a given bounded Apollonian circle packing $\mathcal P $, there exists a
constant $ c> 0$ such that the number of circles of curvature at most $ T $ is asymptotic to …

Let G:= SO (n, 1)◦ and< G be a geometrically finite Zariski dense subgroup with critical
exponent δ greater than (n− 1)/2. Under a spectral gap hypothesis on L2 (\G), which is …

Let $ G $ be the identity component of $\mathrm {SO}(n, 1) $, $ n\ge 2$, acting linearly on a
finite-dimensional real vector space $ V $. Consider a vector $ w_0\in V $ such that the …

We discuss a number of natural problems in arithmetic, arising in completely unrelated
settings, which turn out to have a common formulation involving “thin” orbits. These include …

In the unit tangent bundle of noncompact finite volume negatively curved Riemannian
manifolds, we prove the equidistribution towards the measure of maximal entropy for the …

We give an overview of various counting problems for Apollonian circle packings, which turn
out to be related to problems in dynamics and number theory for thin groups. This survey …

Let D− and D+ be properly immersed closed locally convex subsets of a Riemannian
manifold with pinched negative sectional curvature. Using mixing properties of the geodesic …

In this paper, we use iterations of skinning maps on Teichm\" uller spaces to study circle
packings. This allows us to develop a renormalization theory for circle packings whose …

2 Negatively Curved Geometry 2.1 Background on CAT (− 1) spaces................... 23 2.2
Generalised geodesic lines....................... 29 2.3 The unit tangent bundle........................ 31 2.4 …

Let be a Zariski dense Borel–Anosov representation for equal to or. Let be a form of
signature on (where. Let be the corresponding geodesic copy of the Riemannian symmetric …