New Examples Satisfying Ma-Trudinger-Wang Conditions

In this paper, we study the Ma–Trudinger–Wang (MTW) conditions for cost functions c which are of the form c = l ◦ d, where d is a Riemannian distance function with constant sectional curvature. In this case, the MTW conditions are equivalent to some computable conditions on the function l. As a corollary, we give some new costs on Riemannian manifolds of constant negative curvature for which the MTW conditions are satisfied.