Isometries of spaces of compact or compact convex subsets of metric manifolds |
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Authors: | Prof Dr P M Gruber Dr R Tichy |
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Institution: | (1) Institut für Analysis, Technische Mathematik und Versicherungsmathematik, Technische Universität Wien, Gusshausstrasse 27, A-1040 Wien, Austria |
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Abstract: | The isometries with respect to the Hausdorff metric of spaces of compact or compact convex subsets of certain compact metric spaces are precisely the mappings generated by isometries of the underlying spaces. In particular this holds when the underlying space is a finite dimensional torus or a sphere in a finite dimensional strictly convex smooth normed space. |
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