Hyperbolic geometry was created in the first half of the nineteenth century in the midst of
attempts to understand Euclid's axiomatic basis for geometry. It is one type of non-Euclidean …

We study metric spaces homeomorphic to the 2-sphere, and find conditions under which
they are quasisymmetrically homeomorphic to the standard 2-sphere. As an application of …

This work is devoted to conformal dynamics in metric spaces, it consists of two parts, the first
concerning hyperbolic groups, and the second is the iteration of branched coatings in …

We introduce and study finite subdivision rules. A finite subdivision rule $\mathcal {R} $
consists of a finite 2-dimensional CW complex $ S_ {\mathcal {R}} $, a subdivision $\mathcal …

arXiv:1205.0202v3 [math.GT] 24 Apr 2013 Page 1 arXiv:1205.0202v3 [math.GT] 24 Apr 2013
3-MANIFOLD GROUPS MATTHIAS ASCHENBRENNER, STEFAN FRIEDL, AND HENRY …

This is a survey of recent developments at the interface between quasiconformal analysis
and the asymptotic geometry of Gromov hyperbolic groups. The main theme is the extension …

We study combinatorial modulus on self-similar metric spaces. We give new examples of
hyperbolic groups whose boundaries satisfy a combinatorial version of the Loewner …

The goal of this research monograph is to develop a general combination, decomposition,
and structure theory for branched coverings of the two-sphere to itself, regarded as the …

Le but de cette note est de tenter d'expliquer les liens étroits qui unissent la théorie des
empilements de cercles et des modules combinatoires et de comparer les approches à la …

Suppose $\mathcal {R} $ is an orientation-preserving finite subdivision rule with an edge
pairing. Then the subdivision map $\sigma _ {\mathcal {R}} $ is either a homeomorphism, a …