0.1 Let us start with three equivalent definitions of hyperbolic groups. First observe that for
every finitely presented group r there exists a smooth bounded (Le. bounded by a smooth …

The main theme of this book is the interplay between the behaviour of a class of stochastic
processes (random walks) and discrete structure theory. The author considers Markov …

In this paper we develop some of the foundations of the theory of relatively hyperbolic
groups as originally formulated by Gromov. We prove the equivalence of two definitions of …

A book on the subject of normal families more than sixty years after the publication of
Montel's treatise Ler; ons sur les familles normales de fonc tions analytiques et leurs …

The modern theory of Kleinian groups starts with the work of Lars Ahlfors and Lipman Bers;
specifically with Ahlfors' finiteness theorem, and Bers' observation that their joint work on the …

This book is an introduction to the theory of spatial quasiregular mappings intended for the
uninitiated reader. At the same time the book also addresses specialists in classical analysis …

A Fuchsian group is a discrete subgroup of the group of M6bius transformations on the unit
disk D2 in 1R2. In this paper we characterize up to conjugation in Homeo (Sl) those …

In this paper, we give a construction of the JSJ splitting of a one-ended hyperbolic group (in
the sense of Gromov [Gr]), using the local cut point structure of the boundary. In particular …

We lay the foundations for the study of relatively quasiconvex subgroups of relatively
hyperbolic groups. These foundations require that we first work out a coherent theory of …

We state and prove a combination theorem for relatively hyperbolic groups seen as
geometrically finite convergence groups. For that, we explain how to contruct a boundary for …