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

TL;DR

This paper investigates the Ma-Trudinger-Wang conditions for cost functions composed with Riemannian distance functions on negatively curved spaces, providing new examples where these conditions hold.

Contribution

It establishes computable criteria for MTW conditions on such cost functions and introduces new cost functions satisfying these conditions on negatively curved manifolds.

Findings

Derived explicit conditions for MTW on $c=l\circ d$

Provided new examples of cost functions satisfying MTW on negatively curved spaces

Extended understanding of optimal transport costs in negatively curved geometries

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.