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- W4298727897 abstract "On compact manifolds which are not simply connected, we prove the existence of fake solutions to the optimal transportion problem. These maps preserve volume and arise as the exponential of a closed 1 form, hence appear geometrically like optimal transport maps. The set of such solutions forms a manifold with dimension given by the first Betti number of the manifold. In the process, we prove a Hodge-Helmholtz decomposition for vector fields. The ideas are motivated by the analogies between special Lagrangian submanifolds and solutions to optimal transport problems." @default.
- W4298727897 created "2022-10-02" @default.
- W4298727897 creator A5018547792 @default.
- W4298727897 date "2010-06-07" @default.
- W4298727897 modified "2023-09-27" @default.
- W4298727897 title "A McLean Theorem for the moduli space of Lie solutions to mass transport equations" @default.
- W4298727897 doi "https://doi.org/10.48550/arxiv.1006.1334" @default.
- W4298727897 hasPublicationYear "2010" @default.
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