A full classification of the isometries of the class of ball-bodies
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909524622835712 |
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| author | Artstein-Avidan, Shiri Chor, Arnon Florentin, Dan |
| author_facet | Artstein-Avidan, Shiri Chor, Arnon Florentin, Dan |
| contents | Complementing our previous results, we give a classification of all isometries (not necessarily surjective) of the metric space consisting of ball-bodies, endowed with the Hausdorff metric. "Ball bodies" are convex bodies which are intersections of translates of the Euclidean unit ball. We show that any such isometry is either a rigid motion, or a rigid motion composed with the c-duality mapping. In particular, any isometry on this metric space has to be surjective. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_02613 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A full classification of the isometries of the class of ball-bodies Artstein-Avidan, Shiri Chor, Arnon Florentin, Dan Metric Geometry 52A20, 51F99 Complementing our previous results, we give a classification of all isometries (not necessarily surjective) of the metric space consisting of ball-bodies, endowed with the Hausdorff metric. "Ball bodies" are convex bodies which are intersections of translates of the Euclidean unit ball. We show that any such isometry is either a rigid motion, or a rigid motion composed with the c-duality mapping. In particular, any isometry on this metric space has to be surjective. |
| title | A full classification of the isometries of the class of ball-bodies |
| topic | Metric Geometry 52A20, 51F99 |
| url | https://arxiv.org/abs/2503.02613 |