Fixed point sets of parabolic isometries of CAT(0)-spaces
  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 pi/2, and study its centers. As a consequence, we prove that the set of fixed points is contractible with respect to the Tits topology. 
Koji Fujiwara, Koichi Nagano, Takashi Shioya (Tohoku University)