Isometries of spaces of convex compact subsets of globally non-positively Busemann curved spaces
Tom 103 / 2005
Colloquium Mathematicum 103 (2005), 71-84 MSC: Primary 53C70; Secondary 51F99. DOI: 10.4064/cm103-1-9
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.