Geodesic
Minimal Lagrangian submanifolds of weighted Kim–McCann metrics
Canadian mathematical bulletin, Tome 68 (2025) no. 4, pp. 1223-1238

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DOI

We explore the regularity theory of optimal transport maps for costs satisfying a Ma–Trudinger–Wang condition, by viewing the graphs of the transport maps as maximal Lagrangian surfaces with respect to an appropriate pseudo-Riemannian metric on the product space. We recover the local regularity theory in two-dimensional manifolds.
DOI : 10.4153/S0008439525000487
Mots-clés : Ma–Trudinger–Wang condition, optimal transport, pseudo-Riemannian geometry 
Warren, Micah W. Minimal Lagrangian submanifolds of weighted Kim–McCann metrics. Canadian mathematical bulletin, Tome 68 (2025) no. 4, pp. 1223-1238. doi: 10.4153/S0008439525000487
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     author = {Warren, Micah W.},
     title = {Minimal {Lagrangian} submanifolds of weighted {Kim{\textendash}McCann} metrics},
     journal = {Canadian mathematical bulletin},
     pages = {1223--1238},
     year = {2025},
     volume = {68},
     number = {4},
     doi = {10.4153/S0008439525000487},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439525000487/}
}
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