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

Shiri Artstein-Avidan; Arnon Chor; Dan I. Florentin

doi:10.1112/blms.70203

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

Shiri Artstein-Avidan
, Arnon Chor
, Dan I. Florentin

Department of Mathematics

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 of the (Formula presented.) -duality mapping. In particular, any isometry on this metric space has to be surjective.

Original language	English
Pages (from-to)	3691-3698
Number of pages	8
Journal	Bulletin of the London Mathematical Society
Volume	57
Issue number	12
DOIs	https://doi.org/10.1112/blms.70203
State	Published - Dec 2025

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© 2025 The Author(s). Bulletin of the London Mathematical Society is copyright © London Mathematical Society.

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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. {\textquoteleft}Ball-bodies{\textquoteright} 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 of the (Formula presented.) -duality mapping. In particular, any isometry on this metric space has to be surjective.",

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

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