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arXiv · 1902.10614

Spherical centroid bodies

Florian Besau·Thomas Hack·Peter Pivovarov·Franz E. Schuster
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Abstract

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.

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Florian Besau, Thomas Hack, Peter Pivovarov, Franz E. Schuster. 2019-02-27. Spherical centroid bodies. https://arxiv.org/abs/1902.10614

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