Isometries of spaces of convex compact subsets of CAT(0)-spaces

Thomas Foertsch

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arXiv · math/0404380

Isometries of spaces of convex compact subsets of CAT(0)-spaces

Thomas Foertsch

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Abstract

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.

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Thomas Foertsch. 2004-04-21. Isometries of spaces of convex compact subsets of CAT(0)-spaces. https://arxiv.org/abs/math/0404380

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