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

Jun Kitagawa; Micah Warren

arxiv: 1101.5146 · v3 · pith:4ZYCZOUUnew · submitted 2011-01-26 · 🧮 math.AP · math.DG

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

Jun Kitagawa , Micah Warren This is my paper

classification 🧮 math.AP math.DG

keywords costoptimalproblemsphereconditionsdiffeomorphismdistanceembedded

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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.

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

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