DG-MP-PDE Seminar: Non-negatively cross-curved transportation costs

The theory of optimal transport is concerned with phenomena arising when one matches two mass distributions in a most economic way, minimizing transportation cost of moving mass from one location to another. We consider an optimal transportation problem with costs satisfying certain type of degenerate curvature condition. This condition is a slightly stronger but still degenerate version of the Ma-Trudinger- Wang condition for regularity of optimal transport maps. We explain a continuity result of optimal maps with rough data on local and global domains. If time permits, we will also explain a connection to Principal- Agent problem in microeconomics. These reflect joint work in progress with Alessio Figalli and Robert McCann.