Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 2
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    JAERISCH, JOHANNES 2016. Recurrence and pressure for group extensions. Ergodic Theory and Dynamical Systems, Vol. 36, Issue. 01, p. 108.

    Jaerisch, Johannes 2015. A Lower Bound for the Exponent of Convergence of Normal Subgroups of Kleinian Groups. The Journal of Geometric Analysis, Vol. 25, Issue. 1, p. 298.


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

  • DOI:
  • Published online: 01 April 2009

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.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]M. Culler and P. Shalen . Paradoxical decompositions, 2-generator Kleinian groups, and volumes of hyperbolic 3-manifolds. J. Amer. Math. Soc. 5 (1992), 231288.

[3]E. Fujikawa , K. Matsuzaki and M. Taniguchi . Dynamics on Teichmüller spaces and self-covering of Riemann surfaces. Math. Z. 260(4) (2008), to appear.

[6]K. Matsuzaki . Dynamics of Kleinian groups—the Hausdorff dimension of limit sets. Selected Papers on Classical Analysis (AMS Translation Series (2), 204). The American Mathematical Society, Providence, RI, 2001, pp. 2344.

[7]K. Matsuzaki and Y. Yabuki . Invariance of the Nayatani metrics for Kleinian manifolds. Geom. Dedicata 135 (2008), 147155.

[8]C. McMullen and D. Sullivan . Quasiconformal homeomorphisms and dynamics III. The Teichmüller space of a holomorphic dynamical system. Adv. Math. 135 (1998), 351395.

[9]S. Nayatani . Patterson–Sullivan measure and conformally flat metrics. Math. Z. 225 (1997), 115131.

[13]D. Sullivan . The density at infinity of a discrete group of hyperbolic motions. Publ. Math. Inst. Hautes Études Sci. 50 (1979), 171202.

[15]S. Wang and Q. Zhou . On the proper conjugation of Kleinian groups. Geom. Dedicata 56 (1995), 145154.

[16]X. Wang and W. Yang . Discreteness criteria of Möbius groups of high dimensions and convergence theorems of Kleinian groups. Adv. Math. 159 (2001), 6882.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
Please enter your name
Please enter a valid email address
Who would you like to send this to? *