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- W2949679237 abstract "Building on the results of Ma, Trudinger and Wang cite{MTW}, and of the author cite{L5}, we study two problems of optimal transportation on the sphere: the first corresponds to the cost function $d^2(x,y)$, where $d(cdot,cdot)$ is the Riemannian distance of the round sphere; the second corresponds to the cost function $-log|x-y|$, it is known as the reflector antenna problem. We show that in both cases, the {em cost-sectional curvature} is uniformly positive, and establish the geometrical properties so that the results of cite{L5} and cite{MTW} can apply: global smooth solutions exist for arbitrary smooth positive data and optimal maps are Holder continuous under weak assumptions on the data." @default.
- W2949679237 created "2019-06-27" @default.
- W2949679237 creator A5051304022 @default.
- W2949679237 date "2013-01-26" @default.
- W2949679237 modified "2023-09-27" @default.
- W2949679237 title "Regularity of optimal maps on the sphere: the quadratic cost and the reflector antenna" @default.
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