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/