Optimal transportation on non-compact manifolds

2007/11/28 by Fathi, Albert, Figalli, Alessio · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.0711.4519

Abstract

In this work, we show how to obtain for non-compact manifolds the results that have already been done for Monge Transport Problem for costs coming from Tonelli Lagrangians on compact manifolds. In particular, the already known results for a cost of the type d^r,r>1, where d is the Riemannian distance of a complete Riemannian manifold, hold without any curvature restriction.

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