2023/06/28 by Jun Kitagawa, Kitagawa, Jun, Asuka Takatsu +1
Mathematics · #41A55 #49Q22 #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Optimization and Control (math.OC) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2306.16239
openalex publication_date 2023/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove existence of equal area partitions of the unit sphere via optimal transport methods, accompanied by diameter bounds written in terms of Monge--Kantorovich distances. This can be used to obtain bounds on the expectation of the maximum diameter of partition sets, when points are uniformly sampled from the sphere. An application to the computation of sliced Monge--Kantorovich distances is also presented.