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math.AP2026
Stability of optimal transport maps and second variation of the 2-Monge-Kantorovich distance
F. -U. Caja-Lopez, Matias G. Delgadino, Jun Kitagawa
We establish several quantitative stability estimates for optimal transport maps between non-degenerate densities on uniformly convex domains for the quadratic cost. Under Hölder r…
math.AP2023
Conditions for existence of single valued optimal transport maps on convex boundaries with nontwisted cost
Seonghyeon Jeong, Jun Kitagawa
We prove that if is a (not necessarily strictly) convex, domain, and and are probability measures absolutely continuous with respect t…
math.AP2010★ 2 cited
A parabolic flow toward solutions of the optimal transportation problem on domains with boundary
Jun Kitagawa
We consider a parabolic version of the mass transport problem, and show that it converges to a solution of the original mass transport problem under suitable conditions on the cost…