Seminar

In the Monge--Kantorovich transportation problem, we search for a plan that minimizes the cost of transporting mass from a set of locations  to another set of locations. According to a result of Moser, two volume forms on a compact Manifold of the same total volume are isomorphic and a solution to Monge--Kantorovich  problem offers a special solution to Moser's problem. A celebrated result of Gray asserts that if instead of volume forms we take two contact structures on a compact manifold, then they are isomorphic provided that they can be connected by a smooth arc of contact structures. In this talk, I discuss an optimal transport problem for Gray's result which has a similar flavour as Benamou-Brenier's formulation of  Monge--Kantorovich problem.