Continuity and Injectivity of Optimal Maps
نویسندگان
چکیده
Figalli–Kim–McCann proved in [14] the continuity and injectivity of optimal maps under the assumption (B3) of nonnegative cross-curvature. In the recent [15, 16], they extend their results to the assumption (A3w) of Trudinger-Wang [34], and they prove, moreover, the Hölder continuity of these maps. We give here an alternative and independent proof of the extension to (A3w) of the continuity and injectivity of optimal maps based on the sole arguments of [14] and on new Alexandrov-type estimates for lower bounds.
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