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math.DG2023
Duality of Hessian manifolds and optimal transport
Jakob Hultgren
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-Amp…
math.DG2023
Solvability of Monge-Ampère equations and tropical affine structures on reflexive polytopes
Rolf Andreasson, Jakob Hultgren
Given a reflexive polytope with a height function, we prove a necessary and sufficient condition for solvability of the associated Monge-Ampère equation. When the polytope is Delza…