2019/02/27 by Florian Besau, Besau, Florian, Thomas Hack +5
Mathematics · #28A75 #52A22 #52A40 #52A55 #FOS: Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1902.10614
openalex publication_date 2019/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.