Abstract

We study discrete quasiconformal groups with small dilatation (that is, dilatation close to 1) in n dimensions, n ≥ 3. In particular, we show that under fairly general algebraic assumptions, a discrete quasiconformal group with small dilatation is isomorphic to a discrete group of Möbius transformations. We then analyse under what conditions the algebraic isomorphism is induced by a geometric homeomorphism between the limit sets.

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