For , we prove a global -estimate for potentials of optimal transport maps between convex domains in the plane. Among the tools developed for that purpose are obliqueness in general convex domains and estimates for the growth of eccentricity of sections of the potentials.
"Regularity of optimal transport between planar convex domains." Duke Math. J. 169 (7) 1305 - 1327, 15 May 2020. https://doi.org/10.1215/00127094-2019-0068