arxiv: 1902.10614 · v1 · pith:GWE362MPnew · submitted 2019-02-27 · 🧮 math.MG

Spherical centroid bodies

Florian Besau , Thomas Hack , Peter Pivovarov , Franz E. Schuster This is my paper

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keywords centroidsphericalapproachbodiesbodygeometricprobabilisticalternative

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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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Spherical centroid bodies

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