Spherical centroid bodies
Metric Geometry
2019-02-28 v1
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.
Keywords
Cite
@article{arxiv.1902.10614,
title = {Spherical centroid bodies},
author = {Florian Besau and Thomas Hack and Peter Pivovarov and Franz E. Schuster},
journal= {arXiv preprint arXiv:1902.10614},
year = {2019}
}