Work

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

Year: 2025

Type: article

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 ‐duality mapping. In particular, any isometry on this metric space has to be surjective.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70203

Authors: Shiri Artstein‐Avidan, Arnon Chor, Dan I. Florentin

Institutions: Tel Aviv University, Bar-Ilan University

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: Israel Science Foundation, European Research Council, H2020 European Research Council