Regularity for the optimal transportation problem with Euclidean distance squared cost on the embedded sphere

2011/01/26 by Jun Kitagawa, Kitagawa, Jun, Micah Warren +1 · 1 citation
Mathematics · #35J96 #49Q20 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations #math.AP #math.DG #msc:35J96 #msc:49Q20

paper · pdf · doi:10.48550/arxiv.1101.5146

15 pages. Added gradient estimate depending on Wasserstein distance (see section 5)

openalex publication_date 2011/01/26 · arxiv created 2012/02/04 · arxiv updated 2012/02/07 · openalex created_date 2022/09/26 · openalex updated_date 2026/07/28

Abstract

We give sufficient conditions on initial and target measures supported on the sphere §ⁿ to ensure the solution to the optimal transport problem with the cost |x-y|²/2 is a diffeomorphism.

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• A quantitative stability result for regularity of optimal transport on compact manifolds

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