Spherical centroid bodies

The spherical centroid body of a centrally-symmetric convex body in the Euclidean unit sphere is introduced. Two alternative definitions - one geometric, the other probabilistic in nature - are given and shown to lead to the same objects. The geometric approach is then used to establish a number of...

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Bibliographic Details
Published in:arXiv.org 2019-02
Main Authors: Besau, Florian, Hack, Thomas, Pivovarov, Peter, Schuster, Franz E
Format: Article
Language:English
Subjects:
Convexity
Euclidean geometry
Online Access:Get full text
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Summary:The spherical centroid body of a centrally-symmetric convex body in the Euclidean unit sphere is introduced. Two alternative definitions - one geometric, the other probabilistic in nature - are given and shown to lead to the same objects. The geometric approach is then used to establish a number of basic properties of spherical centroid bodies, while the probabilistic approach inspires the proof of a spherical analogue of the classical polar Busemann-Petty centroid inequality.
ISSN:2331-8422