Duality of Hessian manifolds and optimal transport

2023/06/20 by Jakob Hultgren, Hultgren, Jakob
Mathematics · Physics and Astronomy · #14J33 #32Q25 #35J96 #53A15 #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2306.11819

openalex publication_date 2023/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is an expository paper describing how duality theory for Hessian manifolds provides a natural setting for optimal transport. We explain how this can be used to solve Monge-Ampère equations and survey recent results along these lines with applications to the SYZ-conjecture in mirror symmetry.

Related

• Kantorovich-Rubinstein duality theory for the Hessian
• An optimal transport approach to Monge-Ampère equations on compact Hessian manifolds
• Mass Transportation on Sub-Riemannian Manifolds
• Regularity theory and geometry of unbalanced optimal transport
• A McLean Theorem for the moduli space of Lie solutions to mass transport equations