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

2009/11/20 by Paul W. Y. Lee, Jiayong Li, Lee, Paul W. Y. +1
Mathematics · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Analytic and geometric function theory

paper · pdf · doi:10.48550/arxiv.0911.3978

Abstract

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.

Citations

• Polar factorization and monotone rearrangement of vector‐valued functions
• The Ma-Trudinger-Wang curvature for natural mechanical actions

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