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Optimal transportation on non-compact manifolds

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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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Authors and Affiliations

  1. UMPA, ENS Lyon, 46 Allée d’Italie, 69007, Lyon, France

    Albert Fathi

  2. Scuola Normale Superiore, Piazza dei Cavalieri 7, 56100, Pisa, Italy

    Alessio Figalli

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  1. Albert Fathi
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  2. Alessio Figalli
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Correspondence to Albert Fathi.

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Fathi, A., Figalli, A. Optimal transportation on non-compact manifolds. Isr. J. Math. 175, 1–59 (2010). https://doi.org/10.1007/s11856-010-0001-5

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