A McLean Theorem for the moduli space of Lie solutions to mass transport equations |
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Authors: | Micah Warren |
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Institution: | Department of Mathematics, Princeton University, Princeton, NJ, USA |
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Abstract: | On compact manifolds which are not simply connected, we prove the existence of “fake” solutions to the optimal transportation 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. |
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Keywords: | MSC: 35J96 58D99 58J05 53C38 |
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