English

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

Analysis of PDEs 2012-02-07 v3 Differential Geometry

Abstract

We give sufficient conditions on initial and target measures supported on the sphere §n\S^n to ensure the solution to the optimal transport problem with the cost xy2/2|x-y|^2/2 is a diffeomorphism.

Keywords

Cite

@article{arxiv.1101.5146,
  title  = {Regularity for the optimal transportation problem with Euclidean distance squared cost on the embedded sphere},
  author = {Jun Kitagawa and Micah Warren},
  journal= {arXiv preprint arXiv:1101.5146},
  year   = {2012}
}

Comments

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

R2 v1 2026-06-21T17:17:31.540Z