Fixed point sets of parabolic isometrics of CAT(0)-spaces

Koji Fujiwara, Koichi Nagano, Takashi Shioya

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


We study the fixed point set in the ideal boundary of a parabolic isometry of a proper CAT(0)-space. We show that the radius of the fixed point set is at most π/2, and study its centers. As a consequence, we prove that the set of fixed points is contractible with respect to the Tits topology.

Original languageEnglish
Pages (from-to)305-335
Number of pages31
JournalCommentarii Mathematici Helvetici
Issue number2
Publication statusPublished - 2006


  • CAT(κ)-space
  • Ideal boundary
  • Parabolic isometry
  • Tits metric


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