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research
On the Margulis constant for Kleinian groups, I curvature
Authors
F. W. Gehring
G. J. Martin
Publication date
6 April 1995
Publisher
View
on
arXiv
Abstract
The Margulis constant for Kleinian groups is the smallest constant
c
c
c
such that for each discrete group
G
G
G
and each point
x
x
x
in the upper half space
H
3
{\bold H}^3
H
3
, the group generated by the elements in
G
G
G
which move
x
x
x
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
⟨
f
,
g
⟩
is nonelementary and discrete with
f
f
f
parabolic or elliptic of order
n
≥
3
n \geq 3
n
≥
3
, then every point
x
x
x
in
H
3
{\bold H}^3
H
3
is moved at least distance
c
c
c
by
f
f
f
or
g
g
g
where
c
=
.
1829
…
c=.1829\ldots
c
=
.1829
…
. This bound is sharp
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oai:journal.fi:article/134876
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