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• W3178810195 abstract "Given a compact connected n-dimensional Riemannian manifold, we investigate the smoothness of the optimal transport map between the smooth densities with respect to the squared Riemannian distance cost. The optimal map is characterized by exp(gradu), where the potential function u satisfies a Monge–Ampère type equation. Delanoë [7] showed the smoothness of u on the Riemannian surfaces when the scalar curvature is close to 1 in C 2 norm. In this work, we study the regularity issue on Riemannian manifolds with curvature sufficiently close to curvature of round sphere in C 2 norm in all dimensions and prove that the 𝒞-curvature on such Riemannian manifolds satisfies an improved Ma-Trudinger-Wang condition and the Jacobian of the exponential map is positive. As a consequence, we imply the smoothness of the optimal transport map by the continuity method." @default.
• W3178810195 created "2021-07-19" @default.
• W3178810195 creator A5032700450 @default.
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• W3178810195 date "2021-07-09" @default.
• W3178810195 modified "2023-10-02" @default.
• W3178810195 title "Regularity of optimal transport maps on locally nearly spherical manifolds" @default.
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• W3178810195 doi "https://doi.org/10.5802/afst.1678" @default.
• W3178810195 hasPublicationYear "2021" @default.
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