Kleinian groups and John domains (Q1384302)

A region \(U\) in the Riemann sphere is a John domain if every point in \(U\) can be reached from a fixed basepoint by a flexible cone with a definite angle at its vertex. For every nonelementary, finitely, generated Kleinian group \(\Gamma\), the sphere is naturally partitioned into a limit set \(\Lambda\) and a domain of discontinuity \(\Omega\). In this paper, it is characterized when components \(U\) of \(\Omega\) are John domains and when they are uniformly connected.