Nielsen Methods and Groups Acting on Hyperbolic Spaces

Ilya Kapovich, Richard Weidmann

Research output: Contribution to journalArticlepeer-review


We show that for any n ∈ ℕ there exists a constant C(n) such that any n-generated group G which acts by isometries on a δ-hyperbolic space (with δ > 0) is either free or has a nontrivial element with translation length at most δC(n).

Original languageEnglish (US)
Pages (from-to)95-121
Number of pages27
JournalGeometriae Dedicata
Issue number1
StatePublished - Apr 2003


  • Free groups
  • Group actions
  • Hyperbolic spaces
  • Nielsen methods
  • ℝ-trees

ASJC Scopus subject areas

  • Geometry and Topology


Dive into the research topics of 'Nielsen Methods and Groups Acting on Hyperbolic Spaces'. Together they form a unique fingerprint.

Cite this