Abstract
In the first part of this note, we consider rigid domains which are invariant under certain elementary groups. Each of them corresponds to an isolated point of the set of Schwarzian derivatives of Schlicht functions in the Banach space of the quadratic differentials. Next, we consider “b-group”, that is, a Kleinian group which has a simply connected invariant component. For finitely generated Kleinian groups, all the b-groups are expected to be in the closures of the Bers embeddings of the Teichmüller spaces. We construct two kinds of counterexamples of this conjecture for infinitely generated Kleinian groups.
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