# The intrinsic dynamics of optimal transport

@article{McCann2015TheID, title={The intrinsic dynamics of optimal transport}, author={R. McCann and L. Rifford}, journal={arXiv: Optimization and Control}, year={2015} }

The question of which costs admit unique optimizers in the Monge-Kantorovich problem of optimal transportation between arbitrary probability densities is investigated. For smooth costs and densities on compact manifolds, the only known examples for which the optimal solution is always unique require at least one of the two underlying spaces to be homeomorphic to a sphere. We introduce a (multivalued) dynamics which the transportation cost induces between the target and source space, for which… Expand

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SHOWING 1-10 OF 45 REFERENCES

Abstract Cyclical Monotonicity and Monge Solutions for the General Monge–Kantorovich Problem

- Mathematics
- 1999

Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness

- Mathematics
- 2007