3 papers
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.AP2020
Synthetic MTW conditions and their equivalence under mild regularity assumption on the cost function
Seonghyeon Jeong
Loeper's condition in \cite{Loe09} and the quantitatively quasi-convex condition (QQconv) from \cite{GK15} are synthetic expressions of the analytic MTW condition from \cite{TW} si…
math.AP2020
Hölder regularity of solutions to generated Jacobian equations
Seonghyeon Jeong
Generated Jacobian equations are Monge-Ampère type equations which contain optimal transport as a special case. Therefore, optimal transport case has its own special structure whic…