The Patterson-Sullivan measure and proper conjugation for Kleinian groups of divergence type

Katsuhiko Matsuzaki, Yasuhiro Yabuki

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)657-665
Number of pages9
JournalErgodic Theory and Dynamical Systems
Volume29
Issue number2
DOIs
Publication statusPublished - 2009 Apr 1
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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