a1 Department of Mathematics, Okayama University, Okayama 700-8530, Japan (email: firstname.lastname@example.org)
a2 Mathematical Institute, Tohoku University, Aoba-ku, Sendai 980-8578, Japan (email: email@example.com)
A Kleinian group (a discrete subgroup of conformal automorphisms of the unit ball) G is said to have proper conjugation if it contains the conjugate αGα−1 by some conformal automorphism α as a proper subgroup in it. We show that a Kleinian group of divergence type cannot have proper conjugation. Uniqueness of the Patterson–Sullivan measure for such a Kleinian group is crucial to our proof.
(Received October 09 2007)
(Revised February 26 2008)