Andreasson, Rolf and Hultgren, Jakob and Jonsson, Mattias and Mazzon, Enrica and Mccleerey, Nicholas (2025) Regularity of the Solution to a Real Monge-Ampère Equation on the Boundary of a Simplex. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2025 (3): rnaf013. ISSN 1073-7928, 1687-0247
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Motivated by conjectures in Mirror Symmetry, we continue the study of the real Monge-Amp & egrave;re operator on the boundary of a simplex. This can be formulated in terms of optimal transport, and we consider, more generally, the problem of optimal transport between symmetric probability measures on the boundary of a simplex and of the dual simplex. For suitably regular measures, we obtain regularity properties of the transport map, and of its convex potential. To do so, we exploit boundary regularity results for optimal transport maps by Caffarelli, together with the symmetries of the simplex.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | MONGE-AMPERE EQUATIONS; MIRROR SYMMETRY |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 17 Jun 2026 05:32 |
| Last Modified: | 17 Jun 2026 05:32 |
| URI: | https://pred.uni-regensburg.de/id/eprint/67139 |
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