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

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

2009-11-20

arxiv.org/abs/0911.3978v2

Mathematics

Analysis of PDEs

17 pages

Scientific paper

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.

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