Monge's transport problem on a Riemannian manifold |
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Authors: | Mikhail Feldman Robert J McCann |
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Institution: | Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706 ; Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3 |
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Abstract: | Monge's problem refers to the classical problem of optimally transporting mass: given Borel probability measures , find the measure-preserving map between them which minimizes the average distance transported. Set on a complete, connected, Riemannian manifold -- and assuming absolute continuity of -- an optimal map will be shown to exist. Aspects of its uniqueness are also established. |
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Keywords: | Monge-Kantorovich mass transportation Riemannian manifold optimal map dual problem |
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