Monge's transport problem on a Riemannian manifold

By Mikhail Feldman, Robert J. McCann. 2001

105 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/efe1648e06cb9467429a52efbe3d286f041c93bc

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Optimal transportation on non-compact manifolds (2007, background): “However for the case where the cost is a distance, like in (1), one should cite at least the work of Sudakov [39], Evans-Gangbo [19], Feldman-McCann [23], Caffarelli-Feldman-McCann [11], Ambrosio-Pratelli [5], and Bernard-Buffoni [8].”
Free boundaries in optimal transport and Monge-Ampere obstacle problems (2010, background): “x; y/ D jx yj in particular has attracted recent attention from Ambrosio [7] and Pratelli [9], Ambrosio, Kircheim and Pratelli [5], Caffarelli, Feldman and McCann [20], DePascale, Evans and Pratelli [30], Feldman and McCann [37], [36], and Trudinger and Wang [76] following the work of Evans and Gang”
Monge problem in metric measure spaces with Riemannian curvature-dimension condition (2013, unknown): “The result on manifolds with geodesic cost is obtained in [15].”
Computational Optimal Transport (2018, methodology): “We refer to Feldman and McCann [2002] for a theoretical analysis in the case of X being a Riemannian manifold.”
The globalization theorem for the Curvature-Dimension condition (2016, result): “tation Theory In this section we recall various results from the theory of L1 optimal-transport which are relevant to this work, and add some new information we will subsequently require. We refer to [2, 13, 19, 23, 37, 38, 47, 75] for more details. 47 7.1 Preliminaries To any 1-Lipschitz function u”
Existence and stability results in the L 1 theory of optimal transportation (2003, background): “Afterwards, the first author estabilished in [3] the existence of an optimal transport map assuming only that the initial measure µ is absolutely continuous, and the results of [16] and [42] have been extended to a Riemannian setting in [ 28 ].”
The Monge Problem for Distance Cost in Geodesic Spaces (2011, background): “McCann [10] extended the results to manifolds with geodesic cost.”
Embedding Sn into Rn+1 with given integral Gauss curvature and optimal mass transport on Sn (2007, background): “In our case the transport takes place on a sphere and the cost function (6) does not have a direct analogue among cost functions considered previously in Euclidean space [10], [11], [8] or in Riemannian space [9].”
Optimal transportation, topology and uniqueness (2010, background): “Evans and Gangbo [42] had already solved the analogous problem with the domains replaced by disjoint Lipschitz continuous probability densities, while Sudakov’s [96] earlier construction required a claim which turned out to be true only two in dimensions [4,12]; see [12,23,26] for simplifications an”
Optimal transport maps in Monge-Kantorovich problem (2003, background): “Afterwards, the author estabilished in [2] the existence of an optimal transport map assuming only that the initial measure p is absolutely continuous, and the results of [12] and [34] have been extended to a Riemannian setting in [17].”