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

2025/03/04 by Artstein-Avidan, Shiri, Chor, Arnon, Florentin, Dan · 3 citations
#51F99 #52A20 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2503.02613

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.

Cited by

• Ball-convex bodies and L_p relative surface areas
• A solution to Bezdek's conjecture
• Some inequalities of isoperimetric type for the c-affine surface area

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