We consider the Hausdorff metric on the space of compact convex subsets of a proper, geodesically complete metric space of globally non-positive Busemann curvature in which geodesics do not split, and characterize their surjective isometries. Moreover, an analogous 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 is given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-9, author = {Thomas Foertsch}, title = {Isometries of spaces of convex compact subsets of globally non-positively Busemann curved spaces}, journal = {Colloquium Mathematicae}, volume = {103}, year = {2005}, pages = {71-84}, zbl = {1077.53063}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-9} }
Thomas Foertsch. Isometries of spaces of convex compact subsets of globally non-positively Busemann curved spaces. Colloquium Mathematicae, Tome 103 (2005) pp. 71-84. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-9/