2012/05/14 by Gershon Wolansky, Wolansky, Gershon
Mathematics · #46N10 #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.1205.3078
openalex publication_date 2012/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X a probability measure space and ψ1....ψN measurable, real valued functions on X. Consider all possible partitions of X into N disjoint subdomains Xi on which ∫Xiψi are prescribed. We address the question of characterizing the set (m1,,,mN) ∈ RN for which there exists a partition X1, ...XN of X satisfying ∫Xiψi= mi and discuss some optimization problems on this set of partitions. The relation of this problem to semi-discrete version of optimal mass transportation is discussed as well.