TY - JOUR
T1 - The Patterson-Sullivan measure and proper conjugation for Kleinian groups of divergence type
AU - Matsuzaki, Katsuhiko
AU - Yabuki, Yasuhiro
PY - 2009/4/1
Y1 - 2009/4/1
N2 - 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 PattersonSullivan measure for such a Kleinian group is crucial to our proof.
AB - 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 PattersonSullivan measure for such a Kleinian group is crucial to our proof.
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U2 - 10.1017/S0143385708080267
DO - 10.1017/S0143385708080267
M3 - Article
AN - SCOPUS:69849110343
SN - 0143-3857
VL - 29
SP - 657
EP - 665
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 2
ER -