L¹-Monge problem in metric spaces possibly with branching geodesics

2019/08/02 by Shin-ichiro Kobayashi, Kobayashi, Shinichiro
Mathematics · Physics and Astronomy · #49J45 (Primary) #49K30 #58B20 (Secondary) #Advanced Differential Geometry Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Metric Geometry (math.MG) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1908.00772

openalex publication_date 2019/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the Monge optimal transport problem with distance cost. We prove that in some metric spaces, possibly with many branching geodesics, an optimal transport map exists if the first marginal is absolutely continuous. The result is applicable to normed spaces and Hilbert geometries.

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