, Volume 60, Issue 1, pp 89-127

Families of univalent functions and Kleinian groups

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The paper treats two topics. We obtain new characterizations of quasidiscs using theλ-lemma. We study regularb-groups by combining results on holomorphic families of injections with theorems on algebraic convergence of Kleinian groups and the structure of the Eichler cohomology spaces. We also obtain results about projective structures whose developing maps are coverings.

Research partially supported by NSF grant DMS 8401280.