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arXiv · 2503.02613

A full classification of the isometries of the class of ball-bodies

Shiri Artstein-Avidan·Arnon Chor·Dan Florentin
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Abstract

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.

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Shiri Artstein-Avidan, Arnon Chor, Dan Florentin. 2025-03-04. A full classification of the isometries of the class of ball-bodies. https://arxiv.org/abs/2503.02613

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