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Optimal regularity of optimal transport and degenerations of convex cones
If $T$ is an optimal transport map between bounded convex domains $Ω$ and $Ω'$, we characterize the regularity/singularity dichotomy for $DT$ at $(x,T(x)) \in \partial Ω\times \partial Ω'$. This is obtained through a new approach to the regularity theory based on affine degenerations of the tangent
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