Duality of Hessian manifolds and optimal transport
arXiv:2306.11819
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.
20 pages. Comments are welcome