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Minimal Lagrangian submanifolds of weighted Kim–McCann metrics

Part of: Global differential geometry Manifolds Elliptic equations and systems

Published online by Cambridge University Press:  21 April 2025

Micah W. Warren Open the ORCID record for Micah W. Warren [Opens in a new window]
Micah W. Warren*
Affiliation:
Department of Mathematics, University of Oregon, Eugene, OR 97403, USA
*
e-mail: [email protected]
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Abstract

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.

Keywords

Ma–Trudinger–Wang conditionoptimal transportpseudo-Riemannian geometry

MSC classification

Primary: 49Q20: Variational problems in a geometric measure-theoretic setting 35J96: Elliptic Monge-Ampère equations 53C50: Lorentz manifolds, manifolds with indefinite metrics
Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 16
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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References

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