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arXiv:1101.5146 [math.AP]AbstractReferencesReviewsResources

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

Jun Kitagawa, Micah Warren

Published 2011-01-26, updated 2012-02-04Version 3

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

Comments: 15 pages. Added gradient estimate depending on Wasserstein distance (see section 5)
Categories: math.AP, math.DG
Subjects: 49Q20, 35J96
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