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

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arxiv 2503.02613 v1 pith:I3I32YLU submitted 2025-03-04 math.MG

Shiri Artstein-Avidan , Arnon Chor , Dan Florentin This is my paper · ORCID
classification math.MG
keywords metricballball-bodiesbodiesclassificationisometriesisometrymotion
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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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  1. Some inequalities of isoperimetric type for the c-affine surface area

    math.MG 2025-05 conditional novelty 6.0 of 10

    For ball-bodies, the c-affine surface area is maximized by the ball of radius n/(n+1), and the product with its c-dual is bounded by the squared value at the ball of radius 1/2.

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