On the Margulis constant for Kleinian groups, I curvature

Details On the Margulis constant for Kleinian groups, I curvature On the Margulis constant for Kleinian groups, I curvature

1995-04-07

arxiv.org/abs/math/9504209v1

Mathematics

Differential Geometry

Scientific paper

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

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