A Remark on the Potentials of Optimal Transport Maps

2010/06/20 by Lee, Paul W. Y.
#37J05 #49L99 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1006.3917

Abstract

Optimal maps, solutions to the optimal transportation problems, are completely determined by the corresponding c-convex potential functions. In this paper, we give simple sufficient conditions for a smooth function to be c-convex when the cost is given by minimizing a Lagrangian action.

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