A characterization of Blaschke addition
Richard J. Gardner, Lukas Parapatits, and Franz E. Schuster
TL;DR
This paper characterizes Blaschke addition as a transformation between convex bodies, using a new approach to Minkowski addition and Lévy-Prokhorov metrics, supported by comprehensive examples.
Contribution
It introduces a novel characterization of Blaschke addition based on Minkowski addition and Lévy-Prokhorov metrics, with optimality demonstrated through examples.
Findings
Characterization of Blaschke addition as a map between convex bodies
New characterization of Minkowski addition for zonoids
Examples showing the optimality of the results
Abstract
A characterization of Blaschke addition as a map between origin-symmetric convex bodies is established. This results from a new characterization of Minkowski addition as a map between origin-symmetric zonoids, combined with the use of L\'{e}vy-Prokhorov metrics. A full set of examples is provided that show the results are in a sense the best possible.
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