  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.
