2012/07/17 by Luca Granieri, L. Granieri, Granieri, L. +3
Mathematics · #37J50 #49Q15 #49Q20 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Optimization and Control (math.OC) #math.OC #msc:37J50 #msc:49Q15 #msc:49Q20
paper · pdf · doi:10.48550/arxiv.1207.4026
arxiv created 2012/07/17 · openalex publication_date 2012/07/17 · arxiv updated 2012/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
By disintegration of transport plans it is introduced the notion of transport class. This allows to consider the Monge problem as a particular case of the Kantorovich transport problem, once a transport class is fixed. The transport problem constrained to a fixed transport class is equivalent to an abstract Monge problem over a Wasserstein space of probability measures. Concerning solvability of this kind of constrained problems, it turns out that in some sense the Monge problem corresponds to a lucky case.