20 citations · 37 across the 10 of their papers we have counts for
12 papers
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…
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…
Tropical and non-Archimedean Monge-Ampère equations for a class of Calabi-Yau hypersurfaces
Jakob Hultgren, Mattias Jonsson, Enrica Mazzon +1
For a class of maximally degenerate families of Calabi-Yau hypersurfaces of complex projective space, we study associated non-Archimedean and tropical Monge-Ampère equations, takin…
Optimal Transport for Super Resolution Applied to Astronomy Imaging
Michael Rawson, Jakob Hultgren
Super resolution is an essential tool in optics, especially on interstellar scales, due to physical laws restricting possible imaging resolution. We propose using optimal transport…
Extremal potentials and equilibrium measures associated to collections of Kähler classes
Jakob Hultgren
Given a collection of Kähler forms and a continuous weight on a compact complex manifold we show that it is possible to define natural new notions of extremal potentials and equili…
Mutual Asymptotic Fekete Sequences
Jakob Hultgren
A sequence of point configurations on a compact complex manifold is asymptotically Fekete if it is close to maximizing a sequence of Vandermonde determinants. These Vandermonde det…
Unipotent Factorization of Vector Bundle Automorphisms
Jakob Hultgren, Erlend F. Wold
We provide unipotent factorizations of vector bundle automorphisms of real and complex vector bundles over smooth manifolds. This generalises work of Thurston-Wasserstein and Wasse…
Coupled complex Monge-Ampère equations on Fano horosymmetric manifolds
Thibaut Delcroix, Jakob Hultgren
We give necessary and sufficient conditions for existence of solutions to a general system of complex Monge-Ampère equations on Fano horosymmetric manifolds. In particular, we get…
Coupled Kähler-Ricci solitons on toric Fano manifolds
Jakob Hultgren
We prove a necessary and sufficient condition in terms of the barycenters of a collection of polytopes for existence of coupled Kähler-Einstein metrics on toric Fano manifolds. Thi…
Coupled Kähler-Einstein metrics
Jakob Hultgren, David Witt Nyström
We propose new types of canonical metrics on Kähler manifolds, called coupled Kähler-Einstein metrics, generalizing Kähler-Einstein metrics. We prove existence and uniqueness resul…
An optimal transport approach to Monge-Ampère equations on compact Hessian manifolds
Jakob Hultgren, Magnus Önnheim
In this paper we consider Monge-Ampère equations on compact Hessian manifolds, or equivalently Monge-Ampère equations on certain unbounded convex domains ,…
Permanental Point Processes on Real Tori, Theta Functions and Monge-Ampère Equations
Jakob Hultgren
Inspired by constructions in complex geometry we introduce a thermodynamic framework for Monge-Ampère equations on real tori. We show convergence in law of the associated point pro…