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On the Margulis constant for Kleinian groups, I curvature

Abstract

The Margulis constant for Kleinian groups is the smallest constant cc such that for each discrete group GG and each point xx in the upper half space H3{\bold H}^3, the group generated by the elements in GG which move xx less than distance c is elementary. We take a first step towards determining this constant by proving that if ⟨f,g⟩\langle f,g \rangle is nonelementary and discrete with ff parabolic or elliptic of order n≥3n \geq 3, then every point xx in H3{\bold H}^3 is moved at least distance cc by ff or gg where c=.1829…c=.1829\ldots. This bound is sharp

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