An Obstacle for Higher Regularity of Geodesics in the Space of Kähler Potentials

具有反射障碍物曲面上扭曲测地线的折断射线变换

Broken ray transform for twisted geodesics on surfaces with a reflecting obstacle

本文证明在非正曲率、外力及凸反射障碍条件下，曲面上函数与1-形式之和的扭曲测地线折断射线变换具有唯一性，并推广至磁流等曲线族。

Optimal transport with branching distance costs and the obstacle problem

We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dN is a geodesic Borel distance which makes (X,dN) a possibly branching geodesic space. We show that under some assumptions on the transference plan we can reduce the transport problem to transport problems along family of geodesics. We introduce two assumptions on the transference plan π which imply that the conditional probabilities of the first marginal on each family of geodesics are continuous and that each family of geodesics is a hourglass-like set. We show that this regularity is suffic…