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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 n3n \geq 3, then every point xx in H3{\bold H}^3 is moved at least distance cc by ff or gg where c=.1829c=.1829\ldots. This bound is sharp

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