New examples on spaces of negative sectional curvature satisfying Ma-Trudinger-Wang conditions

Abstract

In this paper, we study the Ma-Trudinger-Wang (MTW) conditions for cost functions $c$ which are of the form $c=l\circ d$, 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.

17 pages

References in corpus (2)

• On strict convexity and $C^1$ regularity of potential functions in optimal transportation
• The Ma-Trudinger-Wang curvature for natural mechanical actions