Normalizer, divergence type, and Patterson measure for discrete groups of the Gromov hyperbolic space

Katsuhiko Matsuzaki, Yasuhiro Yabuki, Johannes Jaerisch

研究成果: Article査読

1 被引用数 (Scopus)

抄録

For a non-elementary discrete isometry group G of divergence type acting on a proper geodesic ı-hyperbolic space, we prove that its Patterson measure is quasi-invariant under the normalizer of G. As applications of this result, we have: (1) under a minor assumption, such a discrete group G admits no proper conjugation, that is, if the conjugate of G is contained in G, then it coincides with G; (2) the critical exponent of any non-elementary normal subgroup of G is strictly greater than half of that for G.

本文言語English
ページ(範囲)369-411
ページ数43
ジャーナルGroups, Geometry, and Dynamics
14
2
DOI
出版ステータスPublished - 2020

ASJC Scopus subject areas

  • 幾何学とトポロジー
  • 離散数学と組合せ数学

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