Open Collections

Mean Curvature flow with respect to Kim-McCann metrics

Banff International Research Station for Mathematical Innovation and Discovery

Given an optimal transportation problem between two manifolds, Kim and McCann offered a pseudo-Riemannian metric on the product manifold, which captures some of the geometry of the problem. By modifying this metric depending on the mass, the graph of the solution is a minimal surface. It is natural to ask then, how mean curvature flow behaves on these manifolds. Work of Li-Salavessa shows that even in high-codimension, mean curvature flow in pseudo-Riemannian spaces can behave remarkably well. We explore this question in both the background-flat case, and in the curved case, where, not surprisingly, we find the Kim-McCann expression of the Ma-Trudinger-Wang condition.

Mathematics; Partial differential equations; Calculus of variations and optimal control; optimization

video/mp4

Author affiliation: University of Oregon

2017-10-11

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63243

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/