Isometries of spaces of convex compact subsets of CAT(0)-spaces
  In the present paper we characterize the surjective isometries of the space of compact, convex subsets of proper, geodesically complete CAT(0)-spaces in which geodesics do not split, endowed with the Hausdorff metric. Moreover, an analogue characterization of the surjective isometries of the space of compact subsets of a proper, uniquely geodesic, geodesically complete metric space in which geodesics do not split, when endowed with the Hausdorff metric, is given. 
Thomas Foertsch