On Semi-discrete Monge Kantorovich and generalized partitions

2012/08/06 by Gershon Wolansky, Wolansky, Gershon
Mathematics · #46n10 #49k30 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Optimization and Control (math.OC) #Point processes and geometric inequalities #math.OC #msc:46n10 #msc:49k30

paper · pdf · doi:10.48550/arxiv.1208.1137

27 pages

arxiv created 2012/08/06 · openalex publication_date 2012/08/06 · arxiv updated 2012/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X a probability measure space and ψ₁....ψ_N measurable, real valued functions on X. Consider all possible partitions of X into N disjoint subdomains X_i on which ∫_Xiψ_i are prescribed. We address the question of characterizing the set (m₁,,,m_N) ∈ \R^N for which there exists a partition X₁, ... X_N of X satisfying ∫_Xiψ_i= m_i 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.

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