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 to ensure the solution to the optimal transport problem with the cost is a diffeomorphism.
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)